Thermodynamics Quiz: State Postulate

20 questions · exam conditions

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State PostulateQuestion 1 of 20

A refrigeration system contains R-134a in a state where the pressure is 0.8 MPa and the specific enthalpy is 250 kJ/kg. An engineer claims that measuring the specific entropy would provide additional independent information about the state. Evaluate this claim using the state postulate.

The claim is correct because entropy provides information about irreversibility that enthalpy cannot capture in refrigeration systems

The claim is incorrect because pressure and specific enthalpy already completely determine the equilibrium state according to the state postulate

The claim is correct because refrigerants require three independent properties due to their complex molecular structure and phase behavior

The claim is incorrect because specific entropy and specific enthalpy are always dependent properties in single-phase refrigerant states

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Thermodynamics Quiz

Thermodynamics Quiz: State Postulate

Practice State Postulate in Thermodynamics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on State Postulate, giving you a quick way to practice the rules, question types, and explanations that matter most for Thermodynamics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The claim is correct because entropy provides information about irreversibility that enthalpy cannot capture in refrigeration systems
The claim is incorrect because pressure and specific enthalpy already completely determine the equilibrium state according to the state postulate (correct answer)
The claim is correct because refrigerants require three independent properties due to their complex molecular structure and phase behavior
The claim is incorrect because specific entropy and specific enthalpy are always dependent properties in single-phase refrigerant states

Explanation: According to the state postulate, two independent intensive properties completely determine the equilibrium state of a simple compressible system. R-134a behaves as a simple compressible substance, so pressure (0.8 MPa) and specific enthalpy (250 kJ/kg) are sufficient to determine all other properties, including specific entropy. Any additional property measurement would be redundant. Choice A is wrong because irreversibility relates to process history, not equilibrium state determination. Choice C is wrong because the state postulate applies regardless of molecular complexity for simple compressible substances. Choice D is wrong because entropy and enthalpy can be independent properties in many states.

Question 2

A rigid tank contains water at $25°C$ and $150 \ \text{kPa}$ . Heat is added to the water until the temperature reaches $75°C$ . To completely specify the final thermodynamic state of the water, what additional property must be determined?

The final pressure, since temperature and specific volume are already known (correct answer)
The final specific enthalpy, since temperature and initial pressure are already known
The final quality, since the water may have undergone a phase change during heating
No additional property is needed, since temperature and pressure uniquely define the state
The final specific entropy, since the process involves irreversible heat transfer

Explanation: When analyzing thermodynamic states, remember that you need two independent intensive properties to completely specify the state of a simple compressible substance. This is a fundamental principle in thermodynamics. Initially, the water is at

25°C

and

150 \text{ kPa}

. Since this is below the saturation temperature at that pressure, the water exists as compressed liquid. The tank is rigid, meaning the volume (and therefore specific volume) remains constant throughout the heating process. As heat is added and temperature rises to

75°C

, the specific volume stays the same while temperature increases. Since you know both the final temperature (

75°C

) and the specific volume (unchanged from initial state), you have two independent properties. However, the final pressure is unknown and will increase due to heating at constant volume. Therefore, the final pressure must be determined to completely specify the thermodynamic state, making answer A correct. Answer B is wrong because specific enthalpy is not an independent property once temperature and specific volume are known—it can be calculated from these. Answer C is incorrect because at

75°C

and the given conditions, the water remains in liquid phase; no phase change occurs. Answer D is wrong because while temperature is known, the final pressure is not—the initial pressure of

150 \text{ kPa}

no longer applies after heating. Study tip: Always identify which properties remain constant in thermodynamic processes (volume in rigid tanks, pressure in pistons, etc.), then count your known independent properties to determine what else you need.

Question 3

An engineer measures the following properties of steam in a turbine: temperature $T = 400°C$ , pressure $P = 3 \ \text{MPa}$ , and specific volume $v = 0.0994 \ \text{m}^3/\text{kg}$ . According to the state postulate, this measurement set is:

Valid because exactly two independent properties are specified for the simple compressible system
Invalid because three properties cannot be independently specified for a simple compressible system (correct answer)
Valid only if the steam is in the superheated region where all three properties are independent
Invalid because specific volume and pressure are always dependent properties in steam systems
Valid because the state postulate requires at least two properties to be measured for verification

Explanation: When you encounter problems involving property measurements in thermodynamics, you need to apply the state postulate, which governs how many independent properties can define a system's state. For simple compressible systems (like steam), exactly two independent intensive properties are sufficient to determine all other properties. The correct answer is B because measuring three properties (temperature, pressure, and specific volume) creates an over-specification problem. In any given state, these three properties are related through an equation of state - once you know any two, the third is automatically determined. The engineer's measurements represent a consistency check rather than an independent specification of state. If the measured values don't align with steam property relationships, it indicates measurement error. Option A incorrectly suggests that having exactly two properties makes this valid, but ignores that three properties were actually measured. Option C contains a fundamental misconception - even in the superheated region, temperature, pressure, and specific volume remain interdependent through the equation of state. No region of the steam tables allows three independent intensive properties. Option D incorrectly singles out specific volume and pressure as "always dependent," when in fact any pair of intensive properties can serve as independent variables. Remember this key principle: for simple compressible systems, any intensive property can be expressed as a function of any two other intensive properties. When you see more than two properties specified, immediately check whether it's a valid two-property state definition or an over-specified (and potentially inconsistent) measurement set.

Question 4

A student claims that for a simple compressible substance, knowing the mass $m = 2 \ \text{kg}$ , volume $V = 0.5 \ \text{m}^3$ , and pressure $P = 200 \ \text{kPa}$ is sufficient to determine the thermodynamic state. This claim is:

Correct, because mass, volume, and pressure provide three independent properties
Incorrect, because mass is an extensive property and cannot be used with the state postulate
Correct, because the specific volume can be calculated and used with pressure to define the state (correct answer)
Incorrect, because volume and pressure are not intensive properties required by the state postulate
Correct, because the given information provides more than the minimum two properties required

Explanation: When you encounter questions about determining thermodynamic states, remember that the state postulate requires knowing two independent intensive properties for a simple compressible substance to fully define its equilibrium state. The student's claim is actually correct because the given information allows calculation of specific volume. With mass

m = 2 \text{ kg}

and volume

V = 0.5 \text{ m}^3

, you can find the specific volume:

v = V/m = 0.5/2 = 0.25 \text{ m}^3/\text{kg}

. Since specific volume is an intensive property (independent of the amount of substance), and pressure

P = 200 \text{ kPa}

is also intensive, you now have two independent intensive properties that fully determine the thermodynamic state. Option A incorrectly suggests that three properties are needed and treats mass as useful for state determination, when only two intensive properties are required. Option B makes a partially correct observation that mass alone cannot define state (since it's extensive), but misses that mass enables calculation of the intensive property specific volume. Option D incorrectly claims that volume and pressure aren't intensive properties—while volume itself is extensive, specific volume (calculated from the given mass and volume) is intensive, and pressure is always intensive. The key insight is recognizing when extensive properties can be converted to intensive ones. Whenever you see mass and volume given together, immediately think "specific volume." This transformation from extensive to intensive properties is a common theme in thermodynamics problems and essential for applying the state postulate correctly.

Question 5

Consider superheated steam at a power plant where the following measurements are recorded: $T = 500°C$ , $h = 3410 \ \text{kJ/kg}$ , and $s = 6.7975 \ \text{kJ/kg⋅K}$ . A thermodynamics student argues that this violates the state postulate because three properties are given. The student's argument is:

Correct, because the state postulate allows only two properties to be specified independently
Incorrect, because all three properties are needed to verify the steam is in the superheated region
Correct, because measuring three properties creates an over-determined system that may be inconsistent (correct answer)
Incorrect, because the state postulate permits additional property measurements for validation purposes
Correct, because enthalpy and entropy are not independent when temperature is specified for superheated steam

Explanation: When you encounter thermodynamic state problems with multiple property measurements, you need to understand the difference between specifying a state and verifying measurements. The state postulate tells us that for a simple compressible substance, specifying two independent intensive properties completely determines the thermodynamic state and all other properties. The student's argument in option C is correct because giving three properties creates a mathematically over-determined system. In thermodynamics, once you specify two independent properties (like temperature and pressure), the third property (enthalpy, entropy, etc.) is automatically fixed by the substance's fundamental relationships. If the measured third property doesn't match the theoretical value calculated from the first two, you have an inconsistency that could indicate measurement errors, calculation mistakes, or that your assumptions about the substance or state are wrong. Option A misunderstands the issue—the state postulate doesn't forbid measuring additional properties, but rather explains why doing so risks inconsistency. Option B incorrectly suggests you need three properties to identify the superheated region, when two independent properties are sufficient to locate any state on property diagrams. Option D wrongly implies the state postulate accommodates extra measurements for validation, when in fact it warns us that over-specification can lead to contradictions. Study tip: Remember that the state postulate is about mathematical consistency, not measurement restrictions. Two independent properties determine the state; additional measurements should be used cautiously and checked for consistency with theoretical values calculated from the first two properties.

Question 6

A gas turbine operates with air modeled as an ideal gas. At a particular state point, the engineer knows the temperature is $800 \ \text{K}$ and wants to determine the minimum additional information needed to calculate all other properties. Which statement correctly identifies this requirement?

Either pressure or density, since ideal gas behavior makes these equivalent choices
Both pressure and specific volume, since ideal gases require two independent intensive properties
Either pressure or specific volume, since either one provides the second independent intensive property (correct answer)
The specific heat ratio, since this determines the relationship between temperature and other properties
Either specific enthalpy or specific entropy, since these are the most fundamental intensive properties

Explanation: When analyzing thermodynamic state points for ideal gases, you need to determine how many independent properties are required to fully define the system's state. The key principle is that any pure substance requires two independent intensive properties to completely specify its thermodynamic state. Since you already know the temperature (

800 \ \text{K}

), you need exactly one more independent intensive property. The ideal gas equation of state,

PV = nRT

P = \rho RT

(where

\rho

is density), shows that pressure, specific volume, and density are all related through temperature. Once you specify any one of these additional properties along with temperature, you can calculate all others using the ideal gas relationships. Choice A is incorrect because while pressure and density are mathematically related for an ideal gas, the question asks for the minimum additional information needed—you don't need to know that they're equivalent choices, just that either one works. Choice B is wrong because it suggests you need both pressure and specific volume, which would give you three total properties (including temperature)—more than the required two independent properties. This represents over-specification. Choice D incorrectly focuses on the specific heat ratio, which affects processes and energy calculations but isn't needed to determine basic state properties like pressure, density, or specific volume from the equation of state. Remember: for any pure substance, two independent intensive properties completely define the thermodynamic state. Count what you have, then determine what's missing to reach that magic number of two.

Question 7

A refrigeration system contains R-134a at $-10°C$ . The technician measures both the pressure ( $P = 201.7 \ \text{kPa}$ ) and finds that the refrigerant is a saturated liquid. Based on the state postulate, this measurement approach is:

Redundant, because specifying saturated liquid at $-10°C$ already determines the pressure (correct answer)
Necessary, because pressure and temperature are always independent properties for refrigerants
Invalid, because quality should be measured instead of pressure for two-phase systems
Required, because both pressure and temperature must be verified to confirm saturation conditions
Incomplete, because the specific volume must also be measured to apply the state postulate

Explanation: When dealing with pure substances in thermodynamic systems, the state postulate tells us that specifying two independent intensive properties completely determines the thermodynamic state. The key word here is "independent" - some property combinations provide redundant information. For a pure substance like R-134a at saturation conditions, temperature and pressure are directly related through the saturation curve. At any given saturation temperature, there's only one corresponding saturation pressure, and vice versa. So when the technician specifies that the refrigerant is saturated liquid at

-10°C

, the pressure is automatically fixed at

201.7 \text{ kPa}

- measuring it provides no additional information about the state. Answer A is correct because once you know the substance is saturated liquid at

-10°C

, the pressure is predetermined by the saturation properties. The measurement is redundant. Answer B is wrong because pressure and temperature are NOT independent at saturation conditions - they're directly related through the Clausius-Clapeyron relationship. Answer C is incorrect because measuring pressure isn't invalid, just unnecessary. Also, for saturated liquid, the quality is zero by definition, so measuring quality would also be redundant. Answer D is wrong because verification isn't the same as determining state properties. While checking measurements might be good practice, it doesn't change the thermodynamic reality that specifying saturated liquid at a given temperature already determines all other intensive properties. Remember: At saturation, temperature and pressure are dependent properties - specifying one automatically determines the other for any pure substance.

Question 8

A closed rigid container holds water that is initially at $20°C$ and $100 \ \text{kPa}$ . Heat is added until the temperature reaches $150°C$ . At the final state, an engineer needs to determine if the water is still liquid, vapor, or a mixture. According to the state postulate, what information is sufficient to make this determination?

The final temperature alone, since the heating process determines the final phase
The final temperature and pressure, since these always determine the phase of water
The final temperature and the initial specific volume, since the container is rigid (correct answer)
The amount of heat added and the final temperature, since energy determines phase changes
The final pressure and the mass of water, since pressure indicates the phase state

Explanation: When analyzing thermodynamic states, the state postulate tells us that specifying two independent intensive properties completely determines the state of a simple compressible substance. The key word here is "independent" - you need properties that can vary separately from each other. In this rigid container problem, you're dealing with a constant volume process. Since the container is rigid, the specific volume cannot change from its initial value. This creates a crucial constraint: while temperature increases to 150°C, the specific volume remains fixed at whatever value corresponds to the initial conditions (20°C, 100 kPa). With both final temperature (150°C) and specific volume known, you have two independent properties that fully define the final state according to the state postulate. You can then use steam tables or property diagrams to determine whether this state point falls in the liquid, vapor, or two-phase region. Option A fails because temperature alone is insufficient - the same temperature can correspond to liquid, vapor, or two-phase states depending on pressure or specific volume. Option B incorrectly assumes you know the final pressure, but pressure will change during heating in a rigid container and isn't given. Option D misses the point entirely - while energy considerations matter for calculating how much phase change occurs, the amount of heat added doesn't directly determine the final phase without knowing the thermodynamic properties. Study tip: In rigid container problems, always remember that specific volume stays constant. This constraint, combined with one other property change, gives you the two independent properties needed to determine any thermodynamic state.

Question 9

A control volume analysis of a heat exchanger requires determining the state of water at the exit where the measured temperature is $90°C$ and pressure is $101.3 \ \text{kPa}$ . A student claims this is insufficient information because water could exist as liquid, vapor, or mixture at these conditions. The student's claim is:

Correct, because additional property measurements are needed to determine the phase
Incorrect, because pressure and temperature always uniquely determine the state for simple substances
Correct, because 90°C is below the saturation temperature at 101.3 kPa, indicating incomplete information
Incorrect, because the given conditions specify a unique state that can be identified using property tables (correct answer)
Correct, because control volume analysis requires additional boundary work information to determine phase

Explanation: When analyzing the state of a substance in thermodynamics, you need to understand how many intensive properties are required to fix the state. For simple substances like water, the state postulate tells us that specifying two independent intensive properties completely determines all other properties. Given temperature

T = 90°C

and pressure

P = 101.3 \text{ kPa}

, you can definitively determine water's state by consulting steam tables. At

101.3 \text{ kPa}

(standard atmospheric pressure), the saturation temperature is

100°C

. Since

90°C < 100°C

, the water exists as compressed (subcooled) liquid. This is a unique, well-defined state where all other properties can be determined from property tables. Choice A incorrectly assumes that two intensive properties are insufficient. While this might be true in the two-phase region where temperature and pressure are dependent, it's false here since we're in the single-phase liquid region. Choice B makes an overly broad claim. Temperature and pressure don't always uniquely determine state - they're dependent properties in two-phase regions, so this reasoning is flawed even though the conclusion happens to be correct for this specific case. Choice C contains a factual error. It claims

90°C

is below the saturation temperature, which is actually correct (

T_{sat} = 100°C

101.3 \text{ kPa}

), but then incorrectly concludes this indicates insufficient information. Being below saturation temperature actually confirms the substance is compressed liquid. Remember: For single-phase regions, any two independent intensive properties fully specify the state. Always check whether your conditions place you in single-phase or two-phase regions first.

Question 10

A laboratory experiment involves heating nitrogen gas in a constant-pressure process from $25°C$ to $200°C$ . The nitrogen is modeled as an ideal gas with constant specific heats. To determine the final state using the state postulate, what properties are known and what additional information is needed?

Final temperature and pressure are known; no additional information is needed to determine the final state (correct answer)
Only final temperature is known; either final pressure or final specific volume must be measured
Final temperature and pressure are known; the initial specific volume must be calculated to determine final state
Final pressure and process path are known; final temperature must be measured to complete state determination
Final temperature is known; the constant-pressure condition provides the final pressure as additional information

Explanation: When analyzing thermodynamic processes, the state postulate is your guiding principle: for a simple compressible system like an ideal gas, knowing any two independent intensive properties completely determines the state. This question tests whether you can identify what constitutes sufficient information. In this constant-pressure heating process, you know both the final temperature (200°C) and final pressure (same as initial pressure, since it's constant-pressure). Since temperature and pressure are two independent intensive properties for an ideal gas, the final state is completely determined by the state postulate. You can calculate any other property you need, such as specific volume using the ideal gas law:

v = \frac{RT}{P}

. Looking at the wrong answers: Option B incorrectly suggests only temperature is known, ignoring that the constant-pressure condition gives you the final pressure. Option C falls into a common trap—thinking you need to calculate initial specific volume to find the final state. While initial volume might be useful for other calculations (like work), it's not required to determine the final state itself. Option D misunderstands what information is actually given, incorrectly stating that final temperature must be measured when it's explicitly provided in the problem. The key insight is distinguishing between "determining a state" versus "analyzing a process." While process analysis might require additional information like initial conditions, state determination only needs two independent intensive properties. Remember: temperature and pressure are always independent for ideal gases, making them sufficient to fix any state.

Question 11

A geothermal power plant uses water as the working fluid. At one state point, the following properties are measured: $T = 180°C$ , $P = 1002 \ \text{kPa}$ , and quality $x = 0.8$ . An engineer questions whether this data set is consistent with the state postulate. The engineer should conclude that:

The data is consistent because temperature, pressure, and quality are all needed for two-phase mixtures
The data is inconsistent because quality is not an intensive property required by the state postulate
The data is consistent because quality and temperature are independent properties in the two-phase region
The data is inconsistent because temperature and pressure are not independent in the saturation region
The data is consistent if the measured pressure equals the saturation pressure at 180°C (correct answer)

Explanation: When analyzing thermodynamic state data, you need to understand the state postulate: the thermodynamic state of a simple system is completely determined by specifying two independent intensive properties. The key word here is "independent." In the two-phase (saturation) region, temperature and pressure are directly related through the saturation relationship - they are not independent. At any given saturation temperature, there's only one corresponding saturation pressure, and vice versa. You can verify this inconsistency by checking steam tables: at

T = 180°C

, the saturation pressure should be approximately 1002.8 kPa, but the given pressure is 1002 kPa, creating a mismatch. Since temperature and pressure aren't independent in the two-phase region, specifying both creates over-constraint of the system. The data set is therefore inconsistent with fundamental thermodynamic principles. Answer A is wrong because while quality is useful for two-phase mixtures, you can't specify three properties (T, P, and x) when only two independent ones are needed. Answer B incorrectly focuses on quality being extensive rather than the real issue of over-specification. Answer C is wrong because temperature and quality aren't independent either - once you know the temperature (which fixes the pressure in two-phase), the specific enthalpy or internal energy determines the quality. Answer D correctly identifies that temperature and pressure aren't independent in the saturation region, making this data set thermodynamically inconsistent. Remember: In the two-phase region, only specify temperature or pressure along with one other intensive property like quality - never both temperature and pressure together.

Question 12

A thermodynamics instructor presents a problem where helium gas undergoes a process in which the initial state is defined by $T_1 = 300 \ \text{K}$ and $P_1 = 150 \ \text{kPa}$ , and the final state is defined by $v_2 = 2v_1$ and $T_2 = 400 \ \text{K}$ . A student argues that the final state violates the state postulate because specific volume is defined relative to the initial state. The student's argument is:

Correct, because relative properties cannot be used as independent intensive properties in the state postulate
Incorrect, because the relationship $v_2 = 2v_1$ allows calculation of the absolute value of $v_2$ (correct answer)
Correct, because the state postulate requires absolute values of intensive properties, not relative relationships
Incorrect, because temperature and the volume ratio provide sufficient independent information to determine the final state
Correct, because helium gas properties cannot be determined without absolute pressure and volume values

Explanation: This question tests your understanding of the state postulate and how to properly define thermodynamic states using intensive properties. The state postulate requires that for a simple compressible system, specifying two independent intensive properties completely determines the state. The student's concern about using

v_2 = 2v_1

is misplaced. While this relationship appears to define specific volume relatively, you can actually determine the absolute value of

v_2

. Using the ideal gas law for the initial state:

P_1v_1 = RT_1

, so

v_1 = \frac{RT_1}{P_1} = \frac{R(300)}{150} = 2R

. Therefore,

v_2 = 2v_1 = 4R

, giving you an absolute value. Combined with

T_2 = 400 \text{ K}

, you have two independent intensive properties that fully define the final state. Option A incorrectly assumes that any relative expression cannot be converted to an absolute property. The mathematical relationship here allows you to calculate the actual specific volume. Option C makes the same error, suggesting the state postulate prohibits relative relationships when the issue is whether you can determine absolute values. Option D is partially correct about having sufficient information but incorrectly identifies "temperature and volume ratio" as the independent properties, when the actual independent properties are the absolute values of specific volume and temperature. Study tip: When evaluating whether thermodynamic states are properly defined, focus on whether you can calculate absolute values of intensive properties, not on how those properties are initially expressed. Mathematical relationships can often convert relative expressions into absolute values.

Question 13

A power plant engineer analyzes steam at turbine conditions where measurements show $P = 4 \ \text{MPa}$ , $T = 400°C$ , and $s = 6.7593 \ \text{kJ/kg⋅K}$ . The engineer wants to use only two properties for state determination to properly follow the state postulate. Which selection criterion should guide this choice?

Choose the two properties with the smallest measurement uncertainty to minimize state determination errors
Choose pressure and temperature because they are primary properties that define all other thermodynamic properties
Choose any two properties and verify that the third property is consistent with steam table data (correct answer)
Choose temperature and entropy because they represent independent fundamental coordinates for the substance
Choose the two properties that are most commonly used in the specific thermodynamic process being analyzed

Explanation: When dealing with state determination problems in thermodynamics, you're applying the state postulate, which says that for a simple compressible substance, specifying two independent intensive properties completely defines the thermodynamic state. The key challenge is ensuring your chosen properties are truly independent and that your measurements are accurate. Option C represents the correct approach because it acknowledges the practical reality of engineering measurements. When you have three measured properties (

P

T

, and

s

), the most reliable method is to select any two properties to determine the state, then verify that the third property matches steam table values within acceptable uncertainty. This cross-checking approach catches measurement errors and confirms state determination accuracy. Option A is flawed because measurement uncertainty alone shouldn't drive property selection—you need properties that are both accurate and independent for your specific state conditions. Option B contains a fundamental misconception: while pressure and temperature are commonly measured properties, they're not always independent. Near the saturation dome or at the critical point,

P

and

T

can be dependent, making state determination impossible with just these two. Option D incorrectly assumes temperature and entropy are universally the best independent coordinates—property independence depends on the specific thermodynamic region and conditions. Remember this strategy: when you have multiple property measurements, use two to determine the state and always verify the remaining properties against reference data. This redundancy catches errors and ensures your state determination is thermodynamically consistent—a crucial skill for any power plant analysis.

Question 14

A chemical plant operates a heat exchanger with water flowing through it. At the inlet, water enters as compressed liquid at $80°C$ and $500 \ \text{kPa}$ . At the outlet, the water temperature has increased to $120°C$ while maintaining the same pressure. An operator claims that the outlet state cannot be determined because the pressure remained constant. The operator's claim is:

Correct, because constant pressure processes require additional information beyond temperature and pressure
Incorrect, because temperature and pressure at the outlet provide two independent intensive properties (correct answer)
Correct, because the outlet water may have vaporized, requiring quality measurement to determine the state
Incorrect, because the process path provides additional constraints that supplement the state postulate requirements
Correct, because heat exchanger analysis requires knowledge of both inlet and outlet states simultaneously

Explanation: When you encounter thermodynamics problems involving state determination, always think about the state postulate: the thermodynamic state of a simple compressible system is completely specified by two independent intensive properties. At the outlet conditions (

120°C

and

500 \text{ kPa}

), you have temperature and pressure—two intensive properties. The key question is whether these are independent. Looking at steam tables, at

500 \text{ kPa}

, the saturation temperature is approximately

151.9°C

. Since the outlet temperature of

120°C

is below this saturation temperature, the water remains in the compressed liquid region where temperature and pressure are independent properties. Therefore, the state is completely determined, making answer B correct. Option A is wrong because constant pressure processes don't require additional information beyond the state postulate requirements. The process path doesn't affect state determination—only the endpoint conditions matter. Option C is incorrect because at

500 \text{ kPa}

and

120°C

, the water cannot have vaporized. Vaporization would only begin at the saturation temperature of

151.9°C

at this pressure. Option D is wrong because while the statement about process constraints might sound sophisticated, it's irrelevant. State determination depends only on having two independent intensive properties at the point of interest, not on the process path. Study tip: Always check whether your temperature is above or below the saturation temperature at the given pressure. This immediately tells you the phase and whether T and P are independent, which is crucial for applying the state postulate correctly.

Question 15

A thermal systems design course presents a problem involving ammonia refrigerant where students must determine the state at the evaporator exit. The given information states: 'saturated vapor at $-15°C$ .' A student questions whether this satisfies the state postulate, arguing that only temperature is specified. The student's argument is:

Correct, because temperature alone is insufficient to determine the thermodynamic state of any substance
Incorrect, because 'saturated vapor' specifies the quality as $x = 1$ , providing a second intensive property (correct answer)
Correct, because saturated vapor could exist at different pressures depending on the system design
Incorrect, because saturation conditions create a unique relationship between temperature and all other properties
Correct, because refrigerant properties require both temperature and pressure measurements for accurate determination

Explanation: When you encounter problems involving thermodynamic states, remember that the state postulate requires two independent intensive properties to fully define the state of a simple compressible substance. The key insight here is recognizing what information is actually provided. The phrase "saturated vapor at

-15°C

" gives you more than just temperature. "Saturated vapor" is a specific thermodynamic condition that means the substance is 100% vapor at the saturation line, which corresponds to a quality of

x = 1

. Quality is an intensive property that describes the fraction of mass in the vapor phase. So you actually have two intensive properties: temperature (

-15°C

) and quality (

x = 1

). This satisfies the state postulate completely. Looking at the wrong answers: Choice A incorrectly assumes only temperature is given, missing that "saturated vapor" provides quality information. Choice C makes the error of thinking saturated vapor conditions are ambiguous - while different pressures can exist for saturated vapor, once you specify the temperature for a pure substance at saturation, the pressure is fixed by the saturation relationship. Choice D is partially correct about saturation creating unique relationships, but uses imprecise language by saying temperature determines "all other properties" rather than identifying the specific second property (quality). The student's confusion likely stems from not recognizing that phase descriptions like "saturated vapor," "saturated liquid," or "wet mixture" contain thermodynamic property information. Always look for these descriptors - they're not just qualitative labels, but quantitative property specifications that help satisfy the state postulate.

Question 16

An engineering student studying a steam power cycle records the following data at the turbine inlet: $P = 6 \ \text{MPa}$ , $T = 600°C$ , $v = 0.05707 \ \text{m}^3/\text{kg}$ , and $h = 3658.4 \ \text{kJ/kg}$ . To properly apply the state postulate for further analysis, the student should:

Use all four properties to ensure the most accurate state determination possible
Select any two of the four properties, since they are all intensive and equally valid
Choose pressure and temperature, since these are the most easily measured properties
Use specific volume and enthalpy, since these avoid potential measurement errors in P and T
Select two properties and verify that the others are consistent with thermodynamic tables (correct answer)

Explanation: When analyzing thermodynamic states, the state postulate is your fundamental guide: for a simple compressible system, specifying two independent intensive properties completely determines the thermodynamic state. The key word here is "independent" – not all property combinations will work. Looking at the given steam data, you need to recognize that at

P = 6

MPa and

T = 600°C

, steam exists as a superheated vapor. In the superheated region, pressure and temperature are independent intensive properties that uniquely define the state. Once you know these two values, all other properties (like specific volume and enthalpy) are automatically determined from steam tables or property relations. Option A suggests using all four properties, but this violates the state postulate – you only need two independent properties, and using more creates redundancy that could reveal measurement inconsistencies. Option B incorrectly assumes any two properties work equally well; while all given properties are intensive, they're not necessarily independent. For instance, in some regions, certain property pairs might not uniquely define the state. Option C correctly identifies that pressure and temperature work, but gives the wrong reasoning – ease of measurement isn't the thermodynamic principle at play. Option D suggests specific volume and enthalpy, which could work in the superheated region, but again uses faulty reasoning about measurement errors. Remember: the state postulate requires exactly two independent intensive properties. For superheated steam, pressure and temperature are the most straightforward choice because they're clearly independent and directly tabulated in steam tables.

Question 17

In a steam power plant analysis, an engineer measures the entropy $s = 6.5 \ \text{kJ/kg⋅K}$ and enthalpy $h = 2700 \ \text{kJ/kg}$ of steam at a particular state point. A colleague argues that these measurements violate the state postulate because both properties depend on the same molecular motion. The colleague's argument is:

Correct, because enthalpy and entropy are thermodynamically dependent properties for steam
Incorrect, because enthalpy and entropy are independent intensive properties that satisfy the state postulate (correct answer)
Correct, because both properties are derived from the same fundamental equation of state
Incorrect, because molecular motion does not determine the independence of thermodynamic properties
Correct, because steam tables show that specifying entropy automatically determines enthalpy

Explanation: When analyzing thermodynamic systems, the state postulate tells us that the equilibrium state of a simple compressible system is completely determined by two independent intensive properties. The key word here is "independent" – the properties must be able to vary independently of each other. Enthalpy and entropy are indeed independent intensive properties for steam. While both are related to molecular energy and motion at the microscopic level, they represent fundamentally different aspects of the thermodynamic state. Entropy measures the degree of molecular disorder or energy dispersal, while enthalpy represents the total energy content including both internal energy and flow work. Most importantly, you can change one without necessarily changing the other in the same proportion – they vary independently during different processes. Option A is incorrect because enthalpy and entropy are not thermodynamically dependent properties. They can vary independently and together uniquely define the state of steam. Option C is wrong because being derived from fundamental equations doesn't make properties dependent – many independent properties come from the same fundamental relationships. Option D is incorrect because while molecular motion doesn't determine independence, the reasoning misses the main point about thermodynamic independence. The colleague's argument fundamentally misunderstands what makes thermodynamic properties independent. Independence isn't about whether properties relate to the same physical phenomena, but whether they can vary independently to uniquely specify a system's state. Study tip: Remember that property independence in thermodynamics is about mathematical relationships and the ability to uniquely define state – not about underlying physical mechanisms.

Question 18

An air conditioning system uses R-22 refrigerant. At the compressor inlet, the technician knows the refrigerant is superheated vapor at $5°C$ with a pressure of $500 \ \text{kPa}$ . A supervisor claims that additional measurements are needed because 'superheated vapor' is not a specific enough description. The supervisor's claim is:

Correct, because the degree of superheat must be quantified with additional temperature measurements
Incorrect, because pressure and temperature are sufficient independent properties for the superheated region (correct answer)
Correct, because superheated vapor requires specification of both temperature and specific volume for complete characterization
Incorrect, because stating 'superheated vapor' provides the quality, which with temperature determines the state
Correct, because refrigerant properties require measurement of enthalpy to distinguish superheated states

Explanation: When determining thermodynamic states, you need to understand how many independent properties are required to fully specify a system's condition. For pure substances in single-phase regions, two independent intensive properties completely define the state. Since you know the refrigerant is at

5°C

and

500 \text{ kPa}

in the superheated vapor region, you have two independent intensive properties (temperature and pressure). These two values completely determine all other thermodynamic properties like specific volume, enthalpy, and entropy using property tables or equations of state. No additional measurements are needed. Option A incorrectly suggests you need to quantify the degree of superheat separately. While superheat degree can be calculated (actual temperature minus saturation temperature at that pressure), it's not required as an additional measurement since you already have the actual temperature. Option C wrongly claims you need specific volume as well. Specific volume is determined once you know temperature and pressure in the superheated region—it's not an independent property you need to measure separately. Option D contains a fundamental misconception by suggesting that "superheated vapor" provides quality. Quality only applies to two-phase (wet) mixtures, not superheated vapor. Superheated vapor exists entirely in the vapor phase, so quality is undefined and irrelevant. Study tip: Remember the "two-property rule" for pure substances in single-phase regions. Once you have two independent intensive properties, the state is completely defined. Quality only applies in the two-phase region between saturated liquid and saturated vapor.

Question 19

A research team studies carbon dioxide near its critical point. They measure $T = 31°C$ , $P = 7.39 \ \text{MPa}$ , and $\rho = 467.6 \ \text{kg/m}^3$ (where $\rho$ is density). A graduate student suggests that near the critical point, the state postulate may not apply because property relationships become highly nonlinear. The student's suggestion is:

Correct, because critical point behavior requires specialized equations that modify the state postulate
Incorrect, because the state postulate applies universally to simple compressible substances regardless of the region (correct answer)
Correct, because density and specific volume provide the same information, creating dependency among properties
Incorrect, because three independent measurements provide better accuracy near critical conditions
Correct, because nonlinear property relationships invalidate the independence assumption of the state postulate

Explanation: When you encounter questions about fundamental thermodynamic principles like the state postulate, focus on understanding what makes this principle universal versus what might seem to challenge it. The state postulate is one of thermodynamics' most fundamental principles: for a simple compressible substance, specifying two independent intensive properties completely determines the thermodynamic state. This principle applies universally to all regions - subcooled liquid, superheated vapor, two-phase mixtures, and yes, even near the critical point. While property relationships become highly nonlinear near critical conditions (causing dramatic changes in properties with small variations in temperature or pressure), this nonlinearity doesn't invalidate the state postulate itself. Option A incorrectly suggests that critical point behavior modifies the state postulate. While specialized equations of state (like cubic equations) are indeed needed for accuracy near critical points, these equations still operate within the framework of the state postulate - they don't change the fundamental requirement of two independent properties. Option C contains a basic misunderstanding. Density and specific volume are reciprocals (

\rho = 1/v

), so they're not independent properties. However, this doesn't affect whether the state postulate applies. Option D incorrectly implies that having three measurements somehow changes the fundamental principle. More measurements might improve accuracy, but the state postulate still requires only two independent intensive properties. Remember: the state postulate is universal for simple compressible substances. Computational complexity or nonlinear behavior doesn't change this fundamental principle - it only affects how we calculate property values.

Question 20

A closed system contains a mixture of liquid water and water vapor in equilibrium at $120°C$ . To apply the state postulate and determine all other thermodynamic properties, which of the following pairs of properties would be sufficient?

Temperature and pressure, since they uniquely define the saturation state
Pressure and specific entropy, since pressure determines temperature in the saturation region (correct answer)
Quality and specific volume, since these directly characterize the two-phase mixture composition
Temperature and specific enthalpy, since temperature is already specified in the problem
Specific internal energy and quality, since both are intensive properties of the mixture

Explanation: When dealing with two-phase systems like this water-vapor mixture, the state postulate requires two independent intensive properties to fully define the thermodynamic state. The key challenge is identifying which properties remain independent in the saturation region. Option B is correct because pressure and specific entropy are independent properties in a two-phase mixture. While pressure does fix the saturation temperature (and vice versa), specific entropy can vary continuously between the saturated liquid and saturated vapor values depending on the quality of the mixture. This makes entropy independent of pressure in the two-phase region, providing the second property needed to determine quality and all other state properties. Option A fails because temperature and pressure are not independent in the saturation region - they're related by the Clausius-Clapeyron equation. Knowing one automatically determines the other, so you only have one independent property, not two. Option C is incorrect because quality and specific volume are not both intensive properties. Quality is intensive, but you need two intensive properties to apply the state postulate properly for determining other intensive properties like temperature and pressure. Option D doesn't work because simply restating that temperature is "specified in the problem" doesn't make temperature and specific enthalpy sufficient. Like with option A, you'd still need to verify these are truly independent properties that can determine the complete state. Study tip: In two-phase regions, remember that temperature and pressure are always dependent on each other. Look for property pairs where one can vary independently while the other is fixed - this usually involves properties that change with quality.