- 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?
Answer: Temperature = 300 K, Pressure = 1 atm, because volume doubles while temperature remains constant
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=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. - 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?
Answer: 7.5 kJ/K, because heat capacity is extensive and scales with the amount of material
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/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. - 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?
Answer: No, because molar volume is intensive and both containers have the same temperature and pressure
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=nV. 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=2n2V=nV - 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=PRT.
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. - 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?
Answer: It remains 150 kJ/kg because specific internal energy is an intensive property
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.
- 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?
Answer: The mass has doubled while the temperature remains unchanged in the combined system
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.
- A thermodynamics student claims that density is an extensive property because "more material means more density." Which analysis of this claim is most accurate?
Answer: The claim is incorrect because density is intensive; it equals mass divided by volume, both of which scale proportionally
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=Vm). 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. - 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?
Answer: Mass = 0.67 kg, Temperature = 300 K, Pressure = 1.5 atm, Volume = 0.4 m³
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.
- 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?
Answer: The student incorrectly treated specific volume as extensive when it is intensive
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.
- When comparing single-unit operation to three-unit operation, which statement correctly distinguishes intensive and extensive property scaling?
Answer: Steam inlet pressure and temperature remain intensive and unchanged, while total power output and steam flow rate triple as extensive properties
Intensive properties (pressure, temperature, efficiency, specific work) remain unchanged when scaling identical systems, while extensive properties (total power, total steam flow) scale proportionally with the number of units. Choice B incorrectly suggests efficiency becomes extensive. Choice C incorrectly states all properties become extensive with scaling. Choice D incorrectly suggests specific work (intensive) increases with more units.
- In a combustion chamber, fuel and air mix at different temperatures before ignition. The fuel enters at 25°C with a mass flow rate of 0.1 kg/s, while air enters at 400°C with a mass flow rate of 2.0 kg/s. Which property analysis correctly applies intensive and extensive concepts to the mixing process?
Answer: The mass-averaged temperature of the mixture is intensive and equals approximately 382°C, while total sensible enthalpy flow rate is extensive
The mass-averaged temperature is intensive (≈ 382°C from energy balance: (0.1×25 + 2.0×400)/(0.1+2.0) = 382.1°C), while total sensible enthalpy flow rate is extensive, scaling with total mass flow. Choice B incorrectly suggests mixture temperature becomes extensive. Choice C incorrectly classifies mass flow rates as intensive - they are extensive properties. Choice D incorrectly suggests temperature averaging requires extensive treatment - the resulting averaged temperature is still an intensive property.
- A refrigeration cycle operates between two thermal reservoirs. The coefficient of performance (COP) is 4.5, and the system removes 100 kW of heat from the cold reservoir while consuming 22.2 kW of work input. Which analysis correctly categorizes these properties?
Answer: COP is intensive as a performance ratio, while heat removal rate and work input are extensive energy flow rates that scale with system size
COP is an intensive property as it represents a performance ratio independent of system size - doubling the system size maintains the same COP. Heat removal rate (100 kW) and work input (22.2 kW) are extensive properties that scale with system size. Choice B incorrectly classifies COP as extensive. Choice C incorrectly suggests that ratios of extensive properties are extensive (they're actually intensive). Choice D incorrectly classifies heat removal rate as intensive and work input as extensive while they're both extensive energy rates.
- 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?
Answer: 600 J/K, because entropy is extensive and scales proportionally with mass
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 2 kg800 J/K=400 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⋅kg=600 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. - During a mixing process, two streams of the same ideal gas at different temperatures combine in a steady-flow mixer. Stream A has twice the mass flow rate of Stream B. Which property relationship is correctly described for the outlet stream?
Answer: The total enthalpy flow rate out equals the sum of total enthalpy flow rates in, demonstrating extensive property behavior
Total enthalpy flow rate (H˙) is an extensive property that obeys conservation principles, so H˙out=H˙A+H˙B. Choice A describes specific enthalpy correctly but doesn't address the extensive nature of total enthalpy flow. Choice B is incorrect because temperature mixing depends on mass flow rates and specific heat capacities. Choice D incorrectly suggests pressure averaging, when outlet pressure is determined by system constraints, not averaging of intensive properties. - Two identical rigid containers, each holding different amounts of the same gas at the same temperature and pressure, are connected by opening a valve between them. Which statement correctly describes the property changes during the equilibration process?
Answer: Final temperature and pressure remain intensive and unchanged, while total entropy increases as an extensive property due to irreversible mixing
Temperature and pressure are always intensive properties and remain unchanged since the gases are identical at the same initial conditions. Total entropy increases due to the irreversible mixing process, demonstrating extensive property behavior. Choice B incorrectly suggests temperature becomes extensive. Choice C incorrectly suggests pressure becomes extensive and that expansion cooling occurs (no temperature change for identical gases). Choice D incorrectly suggests properties can change from intensive to extensive during a process.
- 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?
Answer: It remains 400 W/(m·K) because thermal conductivity is intensive
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.
- 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?
Answer: The error is confusing material properties with flow behavior in different substances
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.
- 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?
Answer: The reasoning is incorrect; the averaging occurs due to energy conservation, not because temperature is extensive
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)cTfinal
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. - 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?
Answer: The temperature will be 25°C because temperature is intensive and independent of the amount of substance
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.
- A steam turbine receives superheated steam at state 1 and discharges at state 2. The specific enthalpy decreases from 3200 kJ/kg to 2400 kJ/kg, while the mass flow rate is 50 kg/s. Which statement correctly distinguishes between intensive and extensive property analysis for this process?
Answer: Specific enthalpy change of -800 kJ/kg is intensive and independent of mass flow rate, while total enthalpy change rate of -40 MW represents extensive property behavior
Specific enthalpy and specific enthalpy change are intensive properties (per unit mass), independent of the total amount of steam. The total enthalpy change rate (m˙Δh=50×(−800)=−40,000 kJ/s = -40 MW) is extensive, scaling with mass flow rate. Choice B incorrectly suggests enthalpy difference is extensive. Choice C incorrectly suggests properties change their intensive/extensive nature during processes. Choice D incorrectly classifies mass flow rate as intensive - it's extensive (total amount per time). - A heat exchanger operates with hot oil flowing through tubes while cold water flows over the tubes. At a specific location, the oil temperature is 150°C and the water temperature is 80°C. Which analysis correctly applies intensive and extensive property concepts to this heat transfer scenario?
Answer: The temperature difference of 70°C is intensive and drives heat transfer, while the total heat transfer rate depends on extensive flow properties
Temperature difference is intensive (independent of system size) and provides the driving force for heat transfer. The total heat transfer rate is extensive, depending on mass flow rates, heat capacities, and heat transfer area. Choice B incorrectly classifies temperatures as extensive. Choice C incorrectly states the heat transfer coefficient is extensive - it's intensive (per unit area). Choice D confuses mathematical operations with property classification - multiplying intensive properties by extensive ones yields extensive results, but doesn't change the nature of the original intensive property.
