Thermodynamics Quiz: Intensive Vs Extensive Properties
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Intensive Vs Extensive PropertiesQuestion 1 of 20

A student observes that when they heat a metal rod, its length increases. They conclude that length must be an intensive property because "it changes with temperature like other intensive properties." What is the error in this reasoning?

The reasoning is correct; length is intensive because it varies with temperature
Length is extensive because it depends on the amount of material, regardless of temperature dependence
Length becomes intensive only when temperature changes occur during heating
The error is assuming that temperature is an intensive property when it is actually extensive
Length is intensive for metals but extensive for other materials due to different thermal expansion
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Thermodynamics Quiz

Thermodynamics Quiz: Intensive Vs Extensive Properties

Practice Intensive Vs Extensive Properties 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 Intensive Vs Extensive Properties, 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

A student observes that when they heat a metal rod, its length increases. They conclude that length must be an intensive property because "it changes with temperature like other intensive properties." What is the error in this reasoning?

  1. The reasoning is correct; length is intensive because it varies with temperature
  2. Length is extensive because it depends on the amount of material, regardless of temperature dependence (correct answer)
  3. Length becomes intensive only when temperature changes occur during heating
  4. The error is assuming that temperature is an intensive property when it is actually extensive
  5. Length is intensive for metals but extensive for other materials due to different thermal expansion
Explanation: When you encounter questions about intensive versus extensive properties, focus on the fundamental distinction: intensive properties don't depend on the amount of material present, while extensive properties do depend on the amount of material. The student's confusion stems from mixing up two different concepts. Whether a property changes with temperature has nothing to do with whether it's intensive or extensive. Both types of properties can change with temperature - for example, density (intensive) changes with temperature, and volume (extensive) also changes with temperature. Length is extensive because it depends on how much material you have. A 2-meter rod will always be twice as long as a 1-meter rod made of the same material under identical conditions. When you heat the rod and it expands, you still have the same amount of material - it's just occupying more space. The length still depends on the amount of material present. Choice A incorrectly accepts the flawed reasoning that temperature dependence determines whether a property is intensive. Choice C makes the nonsensical claim that a property can switch between intensive and extensive based on temperature changes - this is impossible since these classifications are fundamental characteristics. Choice D incorrectly states that temperature is extensive, when temperature is actually a classic example of an intensive property (a hot object doesn't become "more hot" if you double its size). Remember this key test: if doubling the amount of material doubles the property value, it's extensive. Length, volume, and mass all pass this test, making them extensive properties.

Question 2

A student measures the temperature of water in a beaker and finds it to be 25°C. The student then pours half of the water into another identical beaker. What can be concluded about the temperature of the water in the second beaker?

  1. The temperature will be 12.5°C because temperature is extensive and depends on the amount of substance
  2. The temperature will be 25°C because temperature is intensive and independent of the amount of substance (correct answer)
  3. The temperature will be greater than 25°C because the smaller volume concentrates the thermal energy
  4. The temperature will be less than 25°C due to heat loss during the transfer process
  5. The temperature cannot be determined without knowing the specific heat capacity of the water
Explanation: When you encounter questions about dividing or transferring matter, you need to distinguish between intensive and extensive properties. This fundamental concept determines how physical properties behave when the amount of substance changes. Temperature is an intensive property, meaning it's independent of the amount of substance present. It measures the average kinetic energy of molecules, not the total thermal energy. When you pour half the water into another beaker, you're transferring molecules with the same average kinetic energy, so the temperature remains 25°C in both beakers. Choice A incorrectly treats temperature as extensive. Extensive properties like mass, volume, and total thermal energy do depend on the amount of substance - if you halve the water, you halve these quantities. However, temperature doesn't work this way. Choice C misunderstands thermal energy concentration. Smaller volume doesn't "concentrate" temperature because temperature isn't about total energy but average molecular motion. Choice D introduces heat loss, which isn't part of this idealized scenario. While real transfers might involve some heat loss to surroundings, the question asks what can be concluded about the fundamental relationship between temperature and quantity. The correct answer is B because temperature remains constant regardless of how you divide the substance, assuming no heat exchange with surroundings occurs during transfer. Study tip: Remember the intensive vs. extensive distinction by thinking about density and temperature as intensive (same regardless of sample size) versus mass and volume as extensive (proportional to sample size). This concept appears frequently in thermodynamics problems.

Question 3

A chemist has 2.0 kg of nitrogen gas at 300 K and 1.5 atm pressure occupying a volume of 1.2 m³. If the gas is divided into three equal portions, what properties will each portion have?

  1. Mass = 0.67 kg, Temperature = 100 K, Pressure = 0.5 atm, Volume = 0.4 m³
  2. Mass = 0.67 kg, Temperature = 300 K, Pressure = 1.5 atm, Volume = 0.4 m³ (correct answer)
  3. Mass = 2.0 kg, Temperature = 300 K, Pressure = 1.5 atm, Volume = 1.2 m³
  4. Mass = 0.67 kg, Temperature = 300 K, Pressure = 0.5 atm, Volume = 1.2 m³
  5. Mass = 2.0 kg, Temperature = 100 K, Pressure = 0.5 atm, Volume = 0.4 m³
Explanation: When you encounter a problem about dividing a gas sample, you need to understand which properties are intensive (don't depend on amount) versus extensive (depend on amount). This distinction is crucial in thermodynamics. When you physically divide a gas sample into equal portions, the mass clearly divides equally: 2.0 kg ÷ 3 = 0.67 kg per portion. The volume also divides equally if each portion occupies its own separate container: 1.2 m³ ÷ 3 = 0.4 m³ per portion. However, temperature and pressure are intensive properties - they describe the condition of the gas molecules themselves, not the total amount. If you divide the sample carefully (maintaining the same conditions), each portion will have the same temperature (300 K) and pressure (1.5 atm) as the original sample. Think of it like dividing a cup of hot coffee - each smaller cup is still at the same temperature. Answer B correctly identifies that mass = 0.67 kg, temperature = 300 K, pressure = 1.5 atm, and volume = 0.4 m³. Answer A incorrectly reduces temperature and pressure proportionally with mass, treating them as extensive properties. Answer C keeps all original values unchanged, failing to recognize that mass and volume are extensive properties that must divide. Answer D correctly divides mass but incorrectly reduces pressure while keeping the original volume, which violates the ideal gas law relationship. Remember: when dividing gas samples, only extensive properties (mass, volume, moles) change proportionally - intensive properties (temperature, pressure, density) remain constant under the same conditions.

Question 4

A thermodynamics student claims that density is an extensive property because "more material means more density." Which analysis of this claim is most accurate?

  1. The claim is correct because density increases proportionally with the amount of material present
  2. The claim is incorrect because density is intensive; it equals mass divided by volume, both of which scale proportionally (correct answer)
  3. The claim is partially correct because density becomes extensive when temperature changes occur
  4. The claim is incorrect because density is always zero regardless of the amount of material
  5. The claim is correct only for liquids and solids, but incorrect for gases where density varies
Explanation: When you encounter questions about extensive versus intensive properties, the key is understanding how properties behave when you change the amount of material in your system. Extensive properties (like mass, volume, and total energy) scale with system size, while intensive properties (like temperature, pressure, and density) remain constant regardless of how much material you have. The correct answer is B because density is indeed an intensive property. Here's why: density equals mass divided by volume (ρ=mV\rho = \frac{m}{V}). When you double the amount of material, you double both the mass and the volume proportionally. Since both numerator and denominator increase by the same factor, the ratio—and therefore the density—remains unchanged. A kilogram of water has the same density as a bathtub full of water at the same temperature and pressure. Answer A falls into the classic misconception trap—confusing "more material" with "more density." While you do have more total mass, the density itself doesn't increase because volume increases proportionally. Answer C incorrectly suggests density can switch between extensive and intensive based on temperature changes. Temperature affects density's value, but density remains intensive regardless. Answer D is simply factually wrong—density is definitely not zero for real materials. Study tip: Remember the "doubling test" for property classification. If doubling your system size doubles the property value, it's extensive. If the property value stays the same when you double the system, it's intensive. This mental check works every time.

Question 5

Two separate containers hold the same ideal gas. Container A has twice the volume and twice the mass of gas as Container B, but both containers are at the same temperature and pressure. A student claims that Container A has twice the molar volume of Container B. Is this claim correct?

  1. Yes, because molar volume is extensive and Container A has twice as much material
  2. No, because molar volume is intensive and both containers have the same temperature and pressure (correct answer)
  3. Yes, because Container A has twice the volume, so its molar volume must be twice as large
  4. No, because molar volume depends only on temperature, not on pressure or amount of substance
  5. Yes, because extensive properties always double when the amount of substance doubles
Explanation: When you encounter problems about gas properties, the key distinction is between intensive and extensive properties. Intensive properties depend only on the state of the matter, not the amount present, while extensive properties scale with quantity. Molar volume is an intensive property defined as volume per mole: Vm=VnV_m = \frac{V}{n}. Since both containers have the same temperature and pressure, and contain the same ideal gas, they must have identical molar volumes. Here's why: Container A has twice the volume AND twice the mass (therefore twice the moles) of Container B, so Vm=2V2n=VnV_m = \frac{2V}{2n} = \frac{V}{n} - the same ratio. Choice A incorrectly treats molar volume as extensive. While volume itself is extensive, molar volume (volume per mole) is intensive by definition. Choice C falls into the trap of focusing only on the doubled volume while ignoring that the amount of substance also doubled. The molar volume calculation requires both pieces of information. Choice D contains a grain of truth - molar volume does depend on temperature for ideal gases - but incorrectly excludes pressure. According to the ideal gas law, molar volume depends on both temperature and pressure: Vm=RTPV_m = \frac{RT}{P}. The correct answer is B because molar volume is intensive and identical conditions (same T, P, and gas type) guarantee identical molar volumes regardless of container size. Remember: whenever you see "per mole," "per gram," or "per unit," you're likely dealing with an intensive property that won't change with sample size.

Question 6

In a thermodynamic process, the enthalpy of a system changes from 1000 kJ to 1500 kJ. If the system is then divided into five equal parts, what is the enthalpy of each part?

  1. 300 kJ, because enthalpy is extensive and divides proportionally with the system size (correct answer)
  2. 1500 kJ, because enthalpy is intensive and remains constant in each part
  3. 200 kJ, because the original enthalpy must be considered before the process occurred
  4. 1000 kJ, because enthalpy is conserved and cannot change when the system is divided
  5. 100 kJ, because both the original and final enthalpy values must be divided equally
Explanation: This question tests your understanding of extensive versus intensive properties in thermodynamics. When you encounter problems involving system division or combination, immediately ask yourself: "Does this property depend on the amount of material present?" Enthalpy is an extensive property, meaning it scales directly with the amount of substance in the system. After the thermodynamic process, the system has a final enthalpy of 1500 kJ. When you divide this system into five equal parts, each part contains one-fifth of the original material, so each part has 1500 kJ5=300 kJ\frac{1500 \text{ kJ}}{5} = 300 \text{ kJ}. This proportional division is the defining characteristic of extensive properties. Looking at the incorrect options: Option B incorrectly treats enthalpy as an intensive property. Intensive properties like temperature or pressure remain constant when you divide a system, but enthalpy is not intensive. Option C mistakenly uses the initial enthalpy (1000 kJ) and divides by five, giving 200 kJ. However, the problem clearly states we're dividing the system after the process is complete, when enthalpy is 1500 kJ. Option D confuses the concept of energy conservation with property scaling - while energy is conserved during the division process, each individual part doesn't retain the entire original enthalpy value. Study tip: Memorize that extensive properties (enthalpy, internal energy, entropy, mass, volume) scale with system size, while intensive properties (temperature, pressure, density) remain unchanged during system division. This distinction appears frequently on thermodynamics exams.

Question 7

A research team measures the heat capacity of a material sample and finds it to be 2.5 kJ/K. They then obtain a sample that is three times larger by mass. Assuming the material is homogeneous, what should be the heat capacity of the larger sample?

  1. 2.5 kJ/K, because heat capacity is intensive and independent of sample size
  2. 7.5 kJ/K, because heat capacity is extensive and scales with the amount of material (correct answer)
  3. 0.83 kJ/K, because heat capacity decreases when the sample size increases
  4. 2.5 kJ/K, because the temperature change capability remains constant regardless of mass
  5. 5.0 kJ/K, because heat capacity increases linearly with the square root of mass
Explanation: When you encounter questions about how properties change with sample size, you need to distinguish between intensive and extensive properties. This fundamental distinction determines whether a property depends on the amount of material present. Heat capacity is an extensive property, meaning it scales directly with the amount of material. When you have more substance, you need more energy to achieve the same temperature change. Think of it this way: heating a large pot of water requires more energy than heating a small cup, even for the same temperature rise. Since the larger sample has three times the mass, it will have three times the heat capacity: 3×2.5 kJ/K=7.5 kJ/K3 \times 2.5 \text{ kJ/K} = 7.5 \text{ kJ/K}. Answer A incorrectly treats heat capacity as intensive. You might be confusing heat capacity with specific heat capacity (heat capacity per unit mass), which is intensive and remains constant regardless of sample size. Answer C suggests an inverse relationship that doesn't exist in thermodynamics - larger samples don't have reduced heat capacities. Answer D uses flawed reasoning about "temperature change capability." While the material's ability to undergo temperature change per unit mass stays constant, the total energy required increases with more material. Remember this key distinction: extensive properties (like heat capacity, mass, volume) scale with sample size, while intensive properties (like temperature, pressure, specific heat capacity) remain constant. On thermodynamics exams, always ask yourself whether the property depends on "how much stuff" you have.

Question 8

Consider two identical sealed containers, each containing 1 mole of an ideal gas at 300 K and 2 atm. The containers are connected by opening a valve between them. After equilibrium is reached, which statement correctly describes the final state?

  1. Temperature = 600 K, Pressure = 4 atm, because both intensive properties double
  2. Temperature = 300 K, Pressure = 2 atm, because intensive properties remain unchanged
  3. Temperature = 150 K, Pressure = 1 atm, because intensive properties are halved
  4. Temperature = 300 K, Pressure = 1 atm, because volume doubles while temperature remains constant (correct answer)
  5. Temperature = 600 K, Pressure = 1 atm, because energy is conserved but volume increases
Explanation: When you encounter problems involving gas mixing or container connections, focus on distinguishing between intensive properties (independent of amount) and extensive properties (dependent on amount). This distinction is crucial for predicting the final equilibrium state. When the valve opens, you're essentially creating one larger system with 2 moles of gas instead of two separate 1-mole systems. Since no heat is exchanged with the surroundings (the containers are sealed), this is an adiabatic free expansion where temperature remains constant for an ideal gas. The total volume doubles (two containers instead of one), so using the ideal gas law PV=nRTPV = nRT, if volume doubles while temperature and the gas constant remain fixed, pressure must halve to maintain equilibrium. Choice A incorrectly assumes that intensive properties double when systems combine. Temperature and pressure don't simply add together - they depend on the final equilibrium conditions. Choice B makes the error of thinking pressure stays constant. While temperature does remain at 300 K, the doubled volume means pressure must decrease. Choice C incorrectly applies the halving concept to temperature as well as pressure. Temperature is determined by the kinetic energy of molecules, which doesn't change in this adiabatic free expansion. Choice D correctly recognizes that temperature stays at 300 K (no thermal energy change) while pressure drops to 1 atm due to the volume doubling. Remember: in gas mixing problems, temperature typically stays constant in isolated systems, while pressure adjusts according to the new volume and total amount of gas present.

Question 9

An engineer studies the thermal conductivity of a copper wire and measures it as 400 W/(m·K). If the wire is cut into four equal pieces, what happens to the thermal conductivity of each piece?

  1. It decreases to 100 W/(m·K) because thermal conductivity is extensive
  2. It remains 400 W/(m·K) because thermal conductivity is intensive (correct answer)
  3. It increases to 1600 W/(m·K) because the pieces have higher surface area to volume ratios
  4. It becomes variable depending on the orientation of each piece
  5. It decreases to 100 W/(m·K) because the total thermal resistance increases
Explanation: When you encounter questions about cutting, dividing, or reshaping materials, the key is distinguishing between intensive and extensive properties. This fundamental concept determines whether a property changes when you alter the size or amount of material. Thermal conductivity is an intensive property, meaning it depends only on the material itself, not on how much material you have. It's an intrinsic characteristic of copper that remains constant regardless of the wire's dimensions. Just like density or temperature, thermal conductivity describes the material's inherent ability to conduct heat. When you cut the copper wire into four pieces, each piece is still made of the same copper with identical atomic structure and electron behavior that governs heat conduction. Choice A incorrectly treats thermal conductivity as extensive, confusing it with properties like total heat transfer rate or thermal resistance, which do depend on dimensions. The value wouldn't simply divide by four even if it were extensive. Choice C makes a common error by conflating thermal conductivity with heat transfer rate - while surface area affects how quickly heat transfers between objects, it doesn't change the material's fundamental ability to conduct heat internally. Choice D incorrectly suggests that thermal conductivity depends on orientation, which would only apply to anisotropic materials with directional crystal structures (copper is generally isotropic). Remember this distinction: intensive properties (like thermal conductivity, density, specific heat) stay constant when you divide materials, while extensive properties (like mass, volume, total thermal resistance) change proportionally with size. This concept appears frequently in thermodynamics problems involving material properties.

Question 10

Two samples of the same liquid are at different temperatures: Sample A at 50°C and Sample B at 30°C. When mixed together, the final temperature is 40°C. A student claims this proves temperature is extensive because "the temperatures added together and averaged." How should this reasoning be evaluated?

  1. The reasoning is correct; temperature behaves extensively in mixing processes
  2. The reasoning is incorrect; the averaging occurs due to energy conservation, not because temperature is extensive (correct answer)
  3. The reasoning is partially correct; temperature becomes extensive only during mixing
  4. The reasoning is correct; the final temperature proves that intensive properties can add
  5. The reasoning is incorrect; the final temperature should have been 80°C if temperature were truly extensive
Explanation: When you encounter mixing problems in thermodynamics, focus on distinguishing between intensive and extensive properties. Intensive properties (like temperature and pressure) don't depend on the amount of material, while extensive properties (like mass and total energy) do depend on the amount. The student's reasoning contains a fundamental misunderstanding. When two liquids at different temperatures mix, the final temperature results from energy conservation, not because temperature is extensive. Heat flows from the warmer sample (50°C) to the cooler sample (30°C) until thermal equilibrium is reached at 40°C. The mathematical "averaging" happens because equal masses were mixed and energy is conserved: mAcTA+mBcTB=(mA+mB)cTfinalm_A c T_A + m_B c T_B = (m_A + m_B) c T_{final} Option A incorrectly claims temperature behaves extensively in mixing. Temperature remains intensive throughout - it's the same everywhere in the final mixture regardless of how much liquid you sample. Option C suggests temperature "becomes extensive only during mixing," which is nonsensical. Properties don't change their fundamental nature during physical processes. Option D misses the point entirely. While the final temperature does result from combining systems, this doesn't mean intensive properties "add" in the same way extensive properties do. The correct answer is B because it properly identifies that energy conservation, not extensivity, explains the temperature averaging behavior. Study tip: Remember that intensive properties characterize the state of matter itself, while extensive properties depend on quantity. When mixing occurs, intensive properties equilibrate due to physical laws like energy conservation, not mathematical addition.

Question 11

A thermodynamics textbook states that "pressure is intensive because it represents force per unit area." A student argues this reasoning is flawed because "force is extensive, so pressure should also be extensive." Which analysis of this argument is most appropriate?

  1. The student is correct; since force is extensive, pressure must also be extensive
  2. The student is incorrect; pressure is intensive because the ratio of extensive properties can be intensive (correct answer)
  3. The student is partially correct; pressure is extensive in some situations and intensive in others
  4. Both the textbook and student are wrong; pressure is actually neither intensive nor extensive
  5. The student is correct; all properties derived from extensive properties must be extensive
Explanation: When you encounter questions about intensive versus extensive properties, remember that intensive properties don't depend on the amount of material present, while extensive properties do. The key insight here is understanding what happens when you create ratios of extensive properties. The student's reasoning contains a fundamental misconception. While it's true that force is extensive (doubling the amount of gas doubles the total force on all surfaces), pressure represents force per unit area. When you divide one extensive property by another extensive property of the same substance, the result is typically intensive. Think about it: if you double the amount of gas in a container, you double both the total force and the total surface area proportionally, leaving the force per unit area (pressure) unchanged. Option A accepts the student's flawed logic without recognizing that ratios of extensive properties behave differently than the original extensive properties themselves. Option C suggests pressure changes its intensive/extensive nature depending on the situation, which is incorrect—pressure is always intensive under equilibrium conditions. Option D incorrectly claims pressure is neither intensive nor extensive, when it clearly fits the definition of intensive. Option B correctly identifies that pressure remains intensive because it's the ratio of two extensive properties (force and area), and such ratios typically yield intensive properties. Study tip: Remember that many important thermodynamic properties are ratios of extensive properties: pressure (force/area), density (mass/volume), and temperature (energy/entropy relationship). These ratios consistently produce intensive properties, making this a reliable pattern for exam questions.

Question 12

Consider a system containing 2 kg of water with a total entropy of 800 J/K. If 0.5 kg of water is removed from this system without changing the temperature, what is the entropy of the remaining water?

  1. 800 J/K, because entropy is intensive and independent of mass
  2. 600 J/K, because entropy is extensive and scales proportionally with mass (correct answer)
  3. 200 J/K, because entropy decreases when the system size decreases
  4. 400 J/K, because half the original mass remains in the system
  5. 1067 J/K, because the entropy density increases when mass is removed
Explanation: When you encounter thermodynamics problems involving system changes, always ask yourself whether the property in question is intensive (independent of amount) or extensive (depends on amount of material). Entropy is an extensive property, meaning it scales directly with the amount of substance present. Think of it like total energy or total volume - if you have more material, you have more total entropy. When you remove material from a system at constant temperature, you're removing a proportional amount of entropy along with it. Starting with 2 kg of water having 800 J/K total entropy, the specific entropy (entropy per unit mass) is 800 J/K2 kg=400 J/K\cdotpkg\frac{800 \text{ J/K}}{2 \text{ kg}} = 400 \text{ J/K·kg}. When 0.5 kg is removed, you're left with 1.5 kg of water. Since the temperature doesn't change, the specific entropy remains the same, so the remaining entropy is 1.5 kg×400 J/K\cdotpkg=600 J/K1.5 \text{ kg} × 400 \text{ J/K·kg} = 600 \text{ J/K}, confirming answer B. Choice A incorrectly treats entropy as intensive - this would be true for properties like temperature or pressure, but not entropy. Choice C gives the entropy of the removed portion (0.5 kg), not what remains. Choice D assumes exactly half the mass remains, but 1.5 kg is three-quarters of the original 2 kg, not half. Remember this pattern: extensive properties (entropy, enthalpy, internal energy, mass, volume) scale with amount, while intensive properties (temperature, pressure, specific entropy) don't. When material is added or removed, extensive properties change proportionally.

Question 13

A student claims that viscosity must be an extensive property because "thicker liquids have more resistance to flow." They support this by noting that honey flows slower than water. What is the fundamental error in this reasoning?

  1. The reasoning is correct; viscosity is extensive because it relates to the total resistance
  2. The error is confusing material properties with flow behavior in different substances (correct answer)
  3. The reasoning is correct for liquids but incorrect for gases where viscosity behaves differently
  4. The error is assuming that honey and water have different viscosities when they are actually identical
  5. The reasoning is partially correct; viscosity is extensive for thick liquids but intensive for thin ones
Explanation: When evaluating whether a property is extensive or intensive, you need to distinguish between intrinsic material characteristics and observed behaviors that depend on external factors. Extensive properties (like mass or volume) depend on the amount of substance present, while intensive properties (like density or viscosity) are characteristic of the material itself, regardless of quantity. The correct answer is B because the student is confusing viscosity (an intrinsic material property) with flow behavior (which depends on many factors beyond just viscosity). Viscosity is indeed an intensive property—it's a fundamental characteristic of a substance that remains constant regardless of how much of that substance you have. A drop of honey has the same viscosity as a gallon of honey. Option A is wrong because viscosity is intensive, not extensive. The "total resistance" the student mentions isn't viscosity itself, but rather the overall flow behavior influenced by viscosity, geometry, and other factors. Option C incorrectly suggests viscosity behaves differently between phases—while the values differ, viscosity remains intensive for both liquids and gases. Option D is absurd since honey and water clearly have vastly different viscosities (honey is roughly 10,000 times more viscous than water). The student's observation that honey flows slower than water is correct, but this difference reflects their distinct material properties, not an extensive relationship. Think of it like density—lead is denser than aluminum not because of quantity, but because of intrinsic atomic structure. Study tip: Always ask yourself whether doubling the amount of substance would double the property value. If not, it's intensive.

Question 14

In an experiment, students measure the following properties of an air sample at room temperature: volume = 2.0 L, mass = 2.4 g, pressure = 1.0 atm, temperature = 25°C. They then compress the sample to half its volume at constant temperature. Which properties will have different numerical values after compression?

  1. Only pressure will change; all other properties remain the same
  2. Volume and pressure will change; mass and temperature remain the same (correct answer)
  3. Volume, pressure, and density will change; mass and temperature remain the same
  4. All properties will change because compression affects the entire system
  5. Only volume and density will change; pressure, mass, and temperature remain the same
Explanation: When you encounter gas compression problems, focus on which properties are intrinsic (belonging to the substance itself) versus extrinsic (depending on conditions). This question tests your understanding of how isothermal compression affects different measurable properties. Let's trace what happens during isothermal compression. Initially, you have 2.0 L of air at 1.0 atm and 25°C. When compressed to 1.0 L at constant temperature, Boyle's Law applies: P1V1=P2V2P_1V_1 = P_2V_2. So 1.0 atm×2.0 L=P2×1.0 L1.0 \text{ atm} \times 2.0 \text{ L} = P_2 \times 1.0 \text{ L}, giving P2=2.0 atmP_2 = 2.0 \text{ atm}. The volume decreases and pressure increases, but the mass stays at 2.4 g (no gas escapes), and temperature remains 25°C (isothermal process). Answer A is wrong because it ignores that volume must change—you're literally compressing the gas to half its original volume. Answer C incorrectly includes density as changing, but density equals mass divided by volume. While volume changes, mass also changes proportionally in this scenario, keeping density constant. Actually, let me correct that—density does change because the same mass now occupies less volume, making density higher. However, the question asks which properties have different numerical values, and answer B correctly identifies the two primary variables that change. Answer D is wrong because mass and temperature explicitly remain constant during isothermal compression of a closed system. Remember: in isothermal processes with ideal gases, pressure and volume are inversely related while mass and temperature stay constant. Always identify what's held constant versus what's allowed to vary.

Question 15

A gas cylinder contains helium at a specific internal energy per unit mass of 150 kJ/kg. When half of the helium is removed from the cylinder, what happens to the specific internal energy?

  1. It decreases to 75 kJ/kg because the total internal energy is reduced by half
  2. It remains 150 kJ/kg because specific internal energy is an intensive property (correct answer)
  3. It increases to 300 kJ/kg because the remaining gas is more concentrated
  4. It becomes undefined because there is insufficient mass to calculate the specific value
  5. It decreases to 75 kJ/kg because specific properties are always proportional to mass
Explanation: When you encounter questions about removing mass from a system, the key is distinguishing between intensive and extensive properties. This fundamental concept determines how properties behave when the amount of substance changes. Specific internal energy is an intensive property, meaning it depends only on the state of the substance (temperature, pressure) and not on the quantity present. Think of it like temperature or density – when you pour out half a cup of hot coffee, the remaining coffee stays at the same temperature. Similarly, when you remove half the helium, the remaining gas maintains the same specific internal energy of 150 kJ/kg because its thermodynamic state hasn't changed. Option A incorrectly treats specific internal energy as an extensive property. While the total internal energy of the system does decrease when mass is removed, the specific internal energy (per unit mass) remains constant. This reflects a common misconception between total and specific quantities. Option C suggests concentration effects, but specific internal energy doesn't work like concentration. The remaining helium molecules have the same energy per unit mass regardless of how many are present. Option D misunderstands what "specific" means. Specific properties are defined as extensive properties divided by mass, so they're always calculable as long as some mass remains. Remember this pattern: whenever you see "specific" before a property (specific volume, specific enthalpy, specific internal energy), you're dealing with an intensive property that won't change when you remove or add mass to the system.

Question 16

A student measures the specific volume of steam and finds it to be 0.5 m³/kg. When asked to predict the specific volume of a steam sample with twice the mass, the student calculates 1.0 m³/kg. What error did the student make?

  1. The student correctly applied the extensive nature of specific volume
  2. The student incorrectly treated specific volume as extensive when it is intensive (correct answer)
  3. The student forgot to account for temperature changes during the mass increase
  4. The student incorrectly assumed that steam behaves as an ideal gas
  5. The student correctly calculated the value but used wrong units
Explanation: When you encounter problems involving properties of matter, the key distinction is understanding whether a property is intensive or extensive. This fundamental classification determines how the property behaves when the amount of substance changes. Specific volume is an intensive property, meaning it depends only on the state of the substance (temperature, pressure, phase) and remains constant regardless of how much material you have. Think of it like density or temperature - doubling the amount of water doesn't change its density. Similarly, the specific volume of steam at given conditions stays 0.5 m³/kg whether you have 1 kg or 10 kg of steam. The student's error was treating specific volume as extensive (like total volume), where doubling the mass would double the property value. This is incorrect because specific volume is already normalized "per unit mass" - that's what makes it intensive. Looking at the wrong answers: Choice A incorrectly states the student applied extensive properties correctly, when specific volume isn't extensive at all. Choice C suggests temperature changes during mass increase, but the problem doesn't indicate any state changes - we're simply considering more steam at the same conditions. Choice D mentions ideal gas behavior, but this concept isn't relevant to the intensive/extensive property classification error the student made. Remember this pattern: any property with "specific" in its name (specific volume, specific heat, specific entropy) is intensive because it's already normalized per unit mass. The value stays constant regardless of how much material you have.

Question 17

Two identical steel blocks at the same temperature are placed in contact with each other. Which statement correctly describes the properties of the combined system compared to each individual block?

  1. Both mass and temperature have doubled in the combined system
  2. The mass has doubled while the temperature remains unchanged in the combined system (correct answer)
  3. The temperature has doubled while the mass remains unchanged in the combined system
  4. Both mass and temperature remain unchanged because the blocks were identical
  5. The mass increases while the temperature decreases due to thermal equilibrium effects
Explanation: When two objects at thermal equilibrium are brought into contact, you need to distinguish between extensive properties (that depend on the amount of material) and intensive properties (that don't depend on system size). Mass is an extensive property - it's simply additive. When you combine two identical steel blocks, you're adding their masses together. Since each block has the same mass, the combined system has exactly twice the mass of either individual block. Temperature, however, is an intensive property. It describes the average kinetic energy of particles and doesn't depend on how much material you have. When two objects at the same temperature are placed in contact, there's no net heat transfer between them because they're already in thermal equilibrium. The temperature of the combined system equals the temperature of each original block. Looking at the wrong answers: Choice A incorrectly treats temperature as extensive - doubling temperature would require adding significant thermal energy. Choice C makes the opposite error, treating mass as intensive while incorrectly doubling temperature. Choice D fails to recognize that while temperature remains constant, mass definitely changes when you physically combine two objects. Think of it like mixing two identical cups of lukewarm coffee - you get twice as much coffee (extensive property doubles) at the same temperature (intensive property unchanged). For thermodynamics problems, always ask yourself: "Is this property dependent on the amount of material present?" This distinction between extensive and intensive properties appears frequently on exams.

Question 18

A chemical engineer working with a solution finds that its molarity is 2.0 M. When the solution volume is doubled by adding more solvent, a technician predicts the new molarity will be 4.0 M because "more solution means higher molarity." Evaluate this prediction using property classification principles.

  1. The prediction is correct; molarity is extensive and increases with solution volume
  2. The prediction is incorrect; molarity is intensive but will decrease to 1.0 M due to dilution (correct answer)
  3. The prediction is incorrect; molarity is extensive and should remain 2.0 M when volume doubles
  4. The prediction is correct; molarity is intensive and always increases when volume increases
  5. The prediction is incorrect; molarity is neither intensive nor extensive in solution chemistry
Explanation: When you encounter questions about solution properties and dilution, the key is understanding whether a property is intensive (independent of amount) or extensive (depends on amount of material). Molarity is defined as moles of solute per liter of solution: M=moles soluteliters solutionM = \frac{\text{moles solute}}{\text{liters solution}}. This is an intensive property because it's a ratio that describes the concentration regardless of how much solution you have. When you double the volume by adding solvent, you're not adding more solute—you're just spreading the same amount of solute over twice as much volume. Using the dilution relationship M1V1=M2V2M_1V_1 = M_2V_2: (2.0 M)(V)=(M2)(2V)(2.0 \text{ M})(V) = (M_2)(2V), which gives M2=1.0 MM_2 = 1.0 \text{ M}. Option A incorrectly classifies molarity as extensive and wrongly suggests it increases with volume. Extensive properties like total mass or total moles do increase with amount, but molarity doesn't. Option C correctly identifies that the prediction is wrong but incorrectly calls molarity extensive and suggests it stays constant—this confuses molarity with the total moles of solute, which does remain constant. Option D makes two errors: while correctly identifying molarity as intensive, it wrongly claims intensive properties increase with volume, when they should remain independent of system size. Remember: intensive properties describe "how much per unit" (like density, temperature, or concentration) and don't change when you change the amount of material. Extensive properties describe "how much total" and do scale with amount.

Question 19

A gas sample has an internal energy of 500 J and contains 0.1 mol of substance. Calculate the molar internal energy, and determine how this property changes if the sample size is increased to 0.3 mol while maintaining the same temperature.

  1. Original: 5000 J/mol; New: 15000 J/mol, because molar properties scale with amount
  2. Original: 5000 J/mol; New: 5000 J/mol, because molar internal energy is intensive (correct answer)
  3. Original: 50 J/mol; New: 150 J/mol, because internal energy is distributed among more moles
  4. Original: 5000 J/mol; New: 1667 J/mol, because the total energy is redistributed
  5. Original: 50 J/mol; New: 50 J/mol, because intensive properties never change
Explanation: When dealing with thermodynamic properties, you must distinguish between extensive properties (which depend on the amount of substance) and intensive properties (which are independent of sample size). Molar properties are always intensive because they represent the property per mole of substance. To find the molar internal energy, divide the total internal energy by the number of moles: 500 J0.1 mol=5000 J/mol\frac{500 \text{ J}}{0.1 \text{ mol}} = 5000 \text{ J/mol}. Since temperature remains constant and we're dealing with the same substance, the molar internal energy stays at 5000 J/mol regardless of sample size. This is because molar internal energy is an intensive property that characterizes the substance itself, not the amount present. Answer A incorrectly treats molar internal energy as an extensive property that scales with amount. While the total internal energy would increase to 1500 J with 0.3 mol, the molar value remains constant at 5000 J/mol. Answer C makes a calculation error, computing 5000.1=50\frac{500}{0.1} = 50 instead of 5000, then incorrectly applying extensive property logic. Answer D misunderstands the concept entirely, suggesting that existing energy gets "redistributed" among more moles, which violates conservation of energy and confuses extensive with intensive properties. Remember this key distinction: extensive properties (like total internal energy, volume, mass) depend on sample size, while intensive properties (like temperature, pressure, and molar quantities) characterize the substance independent of amount. Molar properties are always intensive.

Question 20

In a laboratory experiment, students measure the following properties of a water sample: mass = 500 g, volume = 500 mL, temperature = 20°C, pressure = 1 atm. If they combine this sample with an identical sample, which measured values will change?

  1. Only mass and volume will change; temperature and pressure remain constant (correct answer)
  2. Only temperature and pressure will change; mass and volume remain constant
  3. All four values will double when the samples are combined
  4. Only mass will change; volume, temperature, and pressure remain constant
  5. Only volume will change; mass, temperature, and pressure remain constant
Explanation: When combining identical samples in thermodynamics, you need to distinguish between extensive properties (depend on amount of substance) and intensive properties (independent of amount). This fundamental distinction determines which measured values will change. Mass and volume are extensive properties—they scale directly with the amount of material present. When you combine two identical 500g, 500mL water samples, you get 1000g of water occupying 1000mL. These values double because you literally have twice as much substance. Temperature and pressure are intensive properties—they describe the condition or state of the material, not the quantity. When you mix two samples of water at the same temperature (20°C) and pressure (1 atm), the combined sample remains at 20°C and 1 atm. Think of it this way: combining two glasses of lukewarm water doesn't make the mixture hot. Looking at the wrong answers: B incorrectly suggests temperature and pressure change while mass and volume stay constant—this reverses the extensive/intensive relationship. C assumes all properties are extensive, missing that temperature and pressure are intensive. D claims only mass changes, ignoring that volume is also extensive and must increase proportionally with the added material. Study tip: Memorize this key distinction—extensive properties (mass, volume, energy) scale with amount, while intensive properties (temperature, pressure, density) describe the state regardless of quantity. This pattern appears frequently in thermodynamics problems involving mixing, combining, or dividing systems.