Question

Which of the following extensive variable will increase during isothermal compression of an ideal gas?

• A. U
• B. S
• C. H
• D. G

Answer 1

Answer: (D)

G

Answer 2

For an ideal gas, internal energy ($U$) and enthalpy ($H$) are functions of temperature only. During isothermal compression, the temperature remains constant, thus $U$ and $H$ are constant.

Entropy ($S$) for an ideal gas changes as $dS = \frac{nR}{V}dV$. During compression, the volume ($V$) decreases, so $dV < 0$. This leads to a decrease in entropy ($dS < 0$).

Gibbs free energy ($G$) changes according to the general relation $dG = VdP - SdT$. During an isothermal process, $dT = 0$, so $dG = VdP$. For an ideal gas undergoing compression, the pressure ($P$) increases ($dP > 0$) while the volume ($V$) is positive. Therefore, $dG > 0$, indicating that Gibbs free energy increases.