An thermally insulated container contains $1 ext{ mol}$ of a liquid having a molar volume of $100

Question

An thermally insulated container contains $1	ext{ mol}$ of a liquid having a molar volume of $100	ext{ mL}$ at $1	ext{ bar}$ pressure. When the liquid is steeply (irreversibly) compressed by applying a constant external pressure of $100	ext{ bar}$, its volume decreases to $99	ext{ mL}$. What are the respective values of the enthalpy change ($\Delta H$) and the change in internal energy ($\Delta U$) for this compression process?

Professor PC Thomas Classes · Answer

Since the container is thermally insulated, $q = 0$. By the first law of thermodynamics, $\Delta U = q + w = w$. Because the pressure is applied steeply, the work done is irreversible against the constant external pressure $P_{	ext{ext}} = 100	ext{ bar}$: $w = -P_{	ext{ext}}(V_2 - V_1) = -100	ext{ bar} 	imes (99 - 100)	ext{ mL} = 100	ext{ bar mL}$. Since $1	ext{ bar L} = 100	ext{ J}$, $1	ext{ bar mL} = 0.1	ext{ J}$. Thus, $\Delta U = 100 	imes 0.1	ext{ J} = 10	ext{ J}$. Now, $\Delta H = \Delta U + (P_2V_2 - P_1V_1) = 100	ext{ bar mL} + (100 	imes 99 - 1 	imes 100)	ext{ bar mL} = 100 + 9900 - 100 = 9900	ext{ bar mL} = 990	ext{ J}$.