For a monatomic ideal gas undergoing an isothermal process, the total internal energy is U = (3/2)NkT, where N is the number of atoms. Since T does not change during this process, what does the source conclude about ΔU and about the relationship between Q and W?
AΔU is negative overall, and Q exceeds W
BΔU is positive overall, and W exceeds Q
CΔU cannot be found, so Q and W are incomparable
DΔU is exactly zero overall, and Q equals W
Answer & Solution
Correct answer: D. ΔU is exactly zero overall, and Q equals W
1. The internal energy of a monatomic ideal gas depends only on N, k and T, with no other variable involved.
2. Since T is held fixed throughout an isothermal process and N and k never change, U itself does not change, so ΔU = 0.
3. The first law states ΔU = Q - W, so setting ΔU to zero gives Q = W directly.
4. This rules out options A and B, which both assign ΔU a nonzero value despite temperature staying constant.
5. ΔU is perfectly well defined here, it is simply zero, so option C's claim that no comparison is possible is incorrect.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.2 The First Law of Thermodynamics and Some Simple Processes_
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