A solid copper block at is placed in an open, massive atmosphere at . During the initial exchange, t — Thermodynamics and Thermochemistry Chemistry Question
Question
A solid copper block at $130^\circ\text{C}$ is placed in an open, massive atmosphere at $32^\circ\text{C}$. During the initial exchange, the block reversibly loses $340 \text{ J}$ of heat to the surroundings. Assuming the temperatures of the block and surroundings remain momentarily constant, what is the total entropy change of the universe ($\Delta S_{univ}$) for this initial heat transfer step?
💡 Solution & Explanation
Convert given temperatures to absolute Kelvin: $T_{sys} = 130 + 273 = 403 \text{ K}$, $T_{surr} = 32 + 273 = 305 \text{ K}$. The heat exchanged is: $q_{sys} = -340 \text{ J}$, $q_{surr} = +340 \text{ J}$. Consequently, $\Delta S_{sys} = \frac{-340}{403} \approx -0.84 \text{ J K}^{-1}$. The environment absorbs this heat identically: $\Delta S_{surr} = \frac{+340}{305} \approx +1.11 \text{ J K}^{-1}$. Finally, $\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr} = -0.84 + 1.11 = +0.27 \text{ J K}^{-1}$.