A frictionless piston filled with exactly of an ideal gas expands reversibly from to at a constant t — Thermodynamics and Thermochemistry Chemistry Question
Question
A frictionless piston filled with exactly $0.04 \text{ mol}$ of an ideal gas expands reversibly from $50.0 \text{ mL}$ to $375 \text{ mL}$ at a constant temperature of $37.0^\circ\text{C}$. During this volume change, it absorbs $208 \text{ J}$ of thermal energy. Calculate the absolute magnitude of the change in internal energy ($\Delta U$) for this entire process in Joules.
💡 Solution & Explanation
The physical process described is maintained at a constant temperature, meaning it is strictly an isothermal process. For any ideal gas, the internal energy is an exclusive function of absolute temperature ($U = f(T)$). Because $\Delta T = 0$ continuously throughout the isothermal expansion, the overall change in internal energy $\Delta U$ remains precisely $0 \text{ J}$. By the First Law of Thermodynamics, all $208 \text{ J}$ of absorbed heat must be exhausted as expansion work ($q = -w$).