Question

$100kJ$ heat is transferred from a larger heat reservoir at $400K$ to another large heat reservoir at $300K$. Suppose there is no change in temperature due to exchange of heat:
Find (a) $\Delta S_{source}$, (b) $\Delta S_{sink}$ and (c) $\Delta S_{total}$. Comment on spontaneity of process:

Answer 1

$\Delta S_{seure}=\frac{q_{reversible}}{T}=\frac{-100\times 1000}{400}=-250$ $J{T}^{-1}$ (Heat is Transferred)

$\Delta S_{sink}=\frac{q_{reversible}}{T}=\frac{100\times 1000}{300}=333.3$ $J{T}^{-1}$

$\Delta S_{Total}=\Delta S_{sink}+\Delta S_{source}$

$⟹\Delta S_{Total}=333.3-250$

$⟹\Delta S_{Total}=83.3$ $J{T}^{-1}$

Since, $\Delta S>0$ process is spontaneous