Free Thermodynamics MCQs with Answers

1. Two bodies are in thermal equilibrium when

• A. they have the same mass
• B. they are at the same temperature, so there is no net flow of heat between them
• C. they contain the same amount of heat
• D. they are made of the same material

Explanation: Temperature is what decides the direction of heat flow, so equal temperatures mean no net transfer even if the two bodies hold very different amounts of internal energy. A cup of tea and a swimming pool at the same temperature are in equilibrium despite the pool storing far more energy. This is the content of the zeroth law, which is what makes a thermometer possible.

2. Heat is best described as

• A. the total energy contained in a body
• B. the temperature of a body
• C. energy in transit from a hotter body to a cooler one because of the temperature difference
• D. a fluid that flows between bodies

Explanation: Heat is a process word: it names energy while it is being transferred, which is why a body is said to contain internal energy rather than to contain heat. Temperature measures the average kinetic energy of the particles and decides which way the transfer goes. The old caloric fluid picture was abandoned once friction was shown to generate heat without limit.

3. The first law of thermodynamics states that the heat supplied to a system equals

• A. the work done by the system alone
• B. the increase in internal energy plus the work done by the system
• C. the fall in internal energy
• D. the temperature rise multiplied by the mass

Explanation: The law is conservation of energy applied to heat: energy entering as heat either raises the internal energy or leaves again as work done on the surroundings. Sign conventions matter, since heat supplied to the system and work done by the system are both counted as positive. A machine that produced work with no energy input would violate this law.

4. In an isothermal expansion of an ideal gas

• A. the internal energy falls
• B. no heat is exchanged
• C. the temperature and therefore the internal energy stay constant, so the heat supplied equals the work done
• D. the work done is zero

Explanation: Constant temperature means constant internal energy for an ideal gas, so by the first law every joule of heat entering leaves again as work done pushing back the surroundings. The process must be slow and the container a good conductor for the temperature to be held fixed. A process with no heat exchange at all is adiabatic, not isothermal.

5. In an adiabatic compression of a gas

• A. the temperature of the gas rises because work is done on it with no heat escaping
• B. the temperature falls
• C. the temperature stays constant
• D. heat flows into the gas from outside

Explanation: With no heat exchange, the work done on the gas must all go into internal energy, so the temperature rises, which is why a bicycle pump warms up when used quickly. Rapid compression is effectively adiabatic because there is no time for heat to escape. The reverse, adiabatic expansion, cools a gas, and that is how clouds form as air rises.

6. For a gas, the molar specific heat at constant pressure Cp is greater than that at constant volume Cv because

• A. the gas is hotter at constant pressure
• B. at constant pressure the gas also does work expanding against the surroundings
• C. the molecules move faster at constant pressure
• D. Cv is measured at a lower temperature

Explanation: At constant volume all the heat supplied raises the internal energy, but at constant pressure some of it is spent doing work as the gas expands, so more heat is needed for the same temperature rise. The difference is exactly the gas constant R, which is Mayer's relation. This is why Cp always exceeds Cv for any gas.

7. The relation between the two molar specific heats of an ideal gas is

• A. Cp minus Cv equals R
• B. Cp plus Cv equals R
• C. Cp times Cv equals R
• D. Cp equals Cv

Explanation: Mayer's relation follows directly from the first law applied to a constant pressure heating, where the extra heat needed is the work of expansion, which for one mole and a one kelvin rise is R. The ratio Cp over Cv, written gamma, is about 1.67 for a monatomic gas and 1.4 for a diatomic one. Gamma governs the speed of sound and adiabatic changes.

8. The second law of thermodynamics implies that

• A. energy can be created in a heat engine
• B. no heat engine can convert all the heat it takes in into work
• C. heat always flows from cold to hot on its own
• D. entropy always decreases

Explanation: Some heat must always be rejected to a cold reservoir, so efficiency is necessarily less than 100 per cent however well the engine is built. Heat flows spontaneously from hot to cold, never the reverse without work being done, which is the other common statement of the same law. The entropy of an isolated system increases or at best stays constant.

9. A Carnot engine operates between reservoirs at 600 K and 300 K. Its maximum possible efficiency is

• A. 20 per cent
• B. 50 per cent
• C. 75 per cent
• D. 100 per cent

Explanation: Carnot efficiency is 1 minus the ratio of the cold to the hot absolute temperature, which is 1 minus 300 over 600, giving 0.5 or 50 per cent. The temperatures must be in kelvin for this to work; using degrees Celsius gives nonsense. No real engine between the same two reservoirs can beat this figure.

10. Absolute zero on the Kelvin scale corresponds to

• A. 0 degrees Celsius
• B. minus 100 degrees Celsius
• C. minus 273 degrees Celsius
• D. minus 373 degrees Celsius

Explanation: Zero kelvin is minus 273.15 degrees Celsius, the temperature at which the pressure of an ideal gas would extrapolate to zero and molecular motion reaches its minimum. Converting between the scales means adding or subtracting 273, since a kelvin and a Celsius degree are the same size. Every gas law formula requires absolute temperature.