A system undergoes a certain change in state by path I and the corresponding heat absorbed and work — Thermodynamics and Thermochemistry Chemistry Question
Question
A system undergoes a certain change in state by path I and the corresponding heat absorbed and work done are 10 kcal and 0 erg, respectively. For the same change in state by path II, the respective quantities are 11 kcal and $0.5 w_{\text{max}}$, where $w_{\text{max}}$ represents the work done if the changes were reversibly carried out. The magnitude of $w_{\text{max}}$ in J, is (1 cal = 4.2 J)
💡 Solution & Explanation
Internal energy is a state function. Path I: $\Delta U = q + w = 10\text{ kcal} + 0 = 10\text{ kcal}$. Path II: $\Delta U = 11\text{ kcal} + 0.5 w_{\text{max}}$. Equating them: $10 = 11 + 0.5 w_{\text{max}} \implies 0.5 w_{\text{max}} = -1\text{ kcal} \implies w_{\text{max}} = -2\text{ kcal}$. The magnitude in Joules is $2 \times 1000 \times 4.2 = 8400\text{ J}$.