An isolated thermodynamic system consisting of of a substance undergoes a process wherein its specif — Thermodynamics and Thermochemistry Chemistry Question
Question
An isolated thermodynamic system consisting of $100 \text{ kg}$ of a substance undergoes a process wherein its specific entropy increases from $0.3 \text{ kJ kg}^{-1}\text{K}^{-1}$ to $0.4 \text{ kJ kg}^{-1}\text{K}^{-1}$. Concurrently, the entropy of the immediate surroundings decreases from $80 \text{ kJ K}^{-1}$ to $75 \text{ kJ K}^{-1}$. Calculate the net total entropy change of the universe ($\Delta S_{univ}$) in $\text{kJ K}^{-1}$.
💡 Solution & Explanation
First, calculate the total absolute entropy change of the isolated system: $\Delta S_{sys} = \text{mass} \times \Delta(\text{specific entropy}) = 100 \text{ kg} \times (0.4 - 0.3) \text{ kJ kg}^{-1}\text{K}^{-1} = 10 \text{ kJ K}^{-1}$. Next, evaluate the entropy change of the thermal surroundings: $\Delta S_{surr} = S_{final} - S_{initial} = 75 - 80 = -5 \text{ kJ K}^{-1}$. Finally, $\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr} = 10 + (-5) = 5 \text{ kJ K}^{-1}$.