State Postulate - Thermodynamics

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?
Answer: Final temperature and pressure are known; no additional information is needed to determine the final state 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.
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?
Answer: The final pressure, since temperature and specific volume are already known 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.
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:
Answer: Incorrect, because the relationship $v_2 = 2v_1$ allows calculation of the absolute value of $v_2$ 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.
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:
Answer: Correct, because the specific volume can be calculated and used with pressure to define the state 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.
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:
Answer: Invalid because three properties cannot be independently specified for a simple compressible system 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.
A thermal energy storage system uses a phase-change material (PCM) that melts at exactly 85°C under atmospheric pressure (101.3 kPa). During operation, sensors indicate the PCM temperature is 85°C and pressure is 101.3 kPa. An engineer argues that the mass fractions of solid and liquid phases must be measured to apply the state postulate correctly. Evaluate this argument.
Answer: The argument is correct because at the phase transition, pressure and temperature are dependent, requiring measurement of phase fraction as the second independent property At the melting point, the system exists in two-phase equilibrium where pressure and temperature are related by the phase equilibrium condition (similar to saturation conditions for liquid-vapor systems). They are not independent properties. To completely specify the state, a second independent intensive property is needed, such as the solid fraction or liquid fraction. This is analogous to needing dryness fraction for wet steam. Choice A is wrong because it assumes P and T are independent at phase transition. Choice B is wrong because only two independent properties are needed, not three. Choice D is wrong because the state postulate applies to all simple compressible substances, including solid-liquid systems.
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:
Answer: Select two properties and verify that the others are consistent with thermodynamic tables 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.
An engineer measures the following properties of a steam sample in a rigid container: pressure = 800 kPa, temperature = 170°C, and dryness fraction = 0.85. According to the state postulate, which statement best describes the independence of these measured properties?
Answer: Only temperature and dryness fraction are independent since pressure depends on temperature in the two-phase region In the two-phase region, pressure and temperature are related by the Clausius-Clapeyron equation - they are not independent. For wet steam, once temperature is specified, the saturation pressure is fixed. However, temperature and dryness fraction are independent properties that can completely determine the state. Choice A is wrong because not all measured properties are necessarily independent. Choice B is wrong because pressure is not independent of temperature in the two-phase region. Choice D is correct in stating that pressure and temperature are dependent, but incorrectly identifies pressure and dryness fraction as the independent pair when temperature and dryness fraction are the independent properties.
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?
Answer: Choose any two properties and verify that the third property is consistent with steam table data 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.
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:
Answer: Incorrect, because pressure and temperature are sufficient independent properties for the superheated region 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.
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:
Answer: Incorrect, because the state postulate applies universally to simple compressible substances regardless of the region 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.
A student analyzing a Rankine cycle determines that at the condenser exit, water exists as saturated liquid at $40°C$ . The student then measures the pressure and finds it to be $7.384 \ \text{kPa}$ . When asked to justify measuring pressure when the state is already specified, the student should explain that:
Answer: Pressure measurement was redundant for state determination but useful for verifying the saturation assumption When analyzing thermodynamic states, understanding the difference between specifying a state and verifying assumptions is crucial. The state postulate tells us that for a simple compressible substance, two independent intensive properties completely determine the thermodynamic state. In this problem, stating "saturated liquid at $40°C$ " actually provides both required properties: temperature ( $40°C$ ) and quality ( $x = 0$ for saturated liquid). This completely specifies the state, and the pressure is automatically fixed at the saturation pressure corresponding to $40°C$ , which happens to be $7.384 \text{ kPa}$ . The pressure measurement serves as verification that the water is indeed saturated, not as a requirement for state determination. Answer A is incorrect because temperature plus the saturation condition (quality = 0) does fully specify the state. Answer C misapplies the state postulate—we already have two independent intensive properties (temperature and quality). Answer D is wrong because distinguishing between saturated and compressed liquid requires knowing that we're at the saturation pressure for the given temperature, which the "saturated liquid" specification already tells us. Answer B correctly identifies that the pressure measurement was redundant for determining the state but valuable for confirming that the saturation assumption holds. If the measured pressure significantly differed from $7.384 \text{ kPa}$ , it would indicate the water isn't actually saturated. Study tip: Remember that stating "saturated" or "superheated" along with one other intensive property gives you the complete state. Additional measurements become verification tools rather than state-determining requirements.
A closed system containing water undergoes a process where the temperature increases from 25°C to 85°C while the pressure remains constant at 200 kPa. If the initial specific volume is 0.001 m³/kg, which combination of properties would be sufficient to completely determine the final state according to the state postulate?
Answer: Temperature and specific volume only, since pressure is already known from the process description According to the state postulate, two independent intensive properties completely determine the equilibrium state of a simple compressible system. Since the final pressure (200 kPa) is given from the process description, we need one additional independent intensive property to determine the final state. Temperature (85°C) provides this second independent property. Choice A is incorrect because we need to determine the final specific volume. Choice C is incorrect because we already know the pressure. Choice D is incorrect because only two independent properties are needed, not three.
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:
Answer: Incorrect, because temperature and pressure at the outlet provide two independent intensive properties 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.
An engineer analyzes a steam power plant where superheated steam at the turbine inlet has a pressure of 8 MPa and temperature of 600°C. The engineer measures the specific volume as 0.0384 m³/kg and finds this value matches property tables. What does this measurement redundancy indicate about the application of the state postulate?
Answer: The matching values demonstrate that specific volume is dependent on pressure and temperature, consistent with the state postulate requiring only two independent properties The state postulate states that two independent intensive properties completely determine all other properties of a simple compressible system in equilibrium. Since pressure (8 MPa) and temperature (600°C) are given, specific volume is completely determined and should match the calculated value from property tables. This redundancy is expected and confirms that specific volume is a dependent property. Choice A misinterprets the measurement as validating equilibrium rather than demonstrating property dependence. Choice B incorrectly suggests that consistent property values indicate error when they actually confirm proper state determination. Choice D focuses on table accuracy rather than the fundamental principle that the third property must be dependent on the first two.
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?
Answer: Either pressure or specific volume, since either one provides the second independent intensive property 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, $PV = nRT$ or $P = \rho RT$ (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.
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:
Answer: Correct, because measuring three properties creates an over-determined system that may be inconsistent 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.
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:
Answer: Redundant, because specifying saturated liquid at $-10°C$ already determines the pressure 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.
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:
Answer: Incorrect, because the given conditions specify a unique state that can be identified using property tables 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 ( $T_{sat} = 100°C$ at $101.3 \text{ kPa}$ ), 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.
During a gas turbine analysis, air enters a combustor at 500 kPa and 300°C with a velocity of 150 m/s. For state determination purposes, which of the following best explains why kinetic energy is not considered when applying the state postulate?
Answer: Kinetic energy is a property of the fluid motion relative to the coordinate system, not an intrinsic property of the thermodynamic state The state postulate deals with intrinsic thermodynamic properties that depend only on the condition of the matter itself, not on its motion relative to a reference frame. Kinetic energy depends on velocity, which is relative to the coordinate system chosen. Temperature (300°C) and pressure (500 kPa) are sufficient to determine the thermodynamic state. Choice A is wrong because the magnitude of kinetic energy doesn't determine whether it's a state property. Choice C is wrong because the state postulate applies to flowing systems - we simply separate kinetic energy in energy analyses. Choice D is wrong because the sonic condition doesn't determine whether kinetic energy is a state property.

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