If the work done on the system or by the system is zero, which one of the following statements for a gas kept at a certain temperature is correct?
- A.Change in internal energy of the system is equal to flow of heat in or out of the system.
- B.Change in internal energy of the system is less than heat transferred.
- C.Change in internal energy of the system is more than the heat flow.
- D.Cannot be determined.
Correct answer
Explanation
The correct answer is A. With no work done, the first law of thermodynamics reduces to ΔU = Q, so the change in internal energy equals the heat that flows in or out.
The first law is a statement of conservation of energy: Q = ΔU + W, where Q is the heat given to the gas, ΔU the change in its internal energy and W the work done by the gas. If W = 0, as when a gas is heated in a rigid closed vessel at constant volume, all the heat supplied goes into raising its internal energy, and all the heat lost comes out of it. This is why the molar heat capacity at constant volume, Cv, measures internal energy directly.
B is wrong because with no work there is nowhere else for part of the heat to go.
C is wrong because internal energy cannot rise by more than the energy supplied.
D is wrong because the first law fixes the relation exactly.
Exam tip: Q = ΔU + W; at constant volume (W = 0), ΔU = Q; in an isothermal ideal gas (ΔU = 0), Q = W.
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