Isothermal Process

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One mole of an ideal gas is compressed isothermally at temperature 300 K, so what happens to its internal energy during this slow compression process?

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Drawing on NCERT Class 11, Chapter 12 (Thermodynamics), for an ideal gas the internal energy depends only on temperature, since the molecules are assumed to have no intermolecular potential energy. In an isothermal process the temperature is held constant, here at 300 K, so the internal energy must stay constant: $\Delta \cup = 0$. This holds whether the gas is compressed or expanded, as long as temperature does not change. Applying the First Law, $\Delta Q = \Delta \cup + \Delta W = 0 + \Delta W$, so all heat exchanged equals the work done; during compression the surroundings do work on the gas and an equal amount of heat is released. The option that internal energy increases with pressure is wrong because internal energy of an ideal gas is not a function of pressure at fixed temperature. The option that it decreases with volume is wrong for the same reason. The option that it doubles when volume halves confuses internal energy with pressure behaviour under Boyle's law. A sanity check: with $\Delta T = 0$ and $U \propto T$ for an ideal gas, $\Delta \cup = 0$ is consistent and dimensionally trivial.

Isothermal Process

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