Try the fastest way to create flashcards
Question

# Find an expression for the change in entropy when two blocks of the same substance and of equal mass, one at the temperature $T_{h}$ the other at $T_{e},$ are brought into thermal contact and allowed to reach equilibrium. Evaluate the change in entropy for two blocks of copper, each of mass 500 g, with $C_{pm}=24.4\ \mathrm{JK}^{-1}\ \mathrm{mol}^{-1},$ taking $T_{\mathrm{h}}=500 \mathrm{K}$ and $T_{e}=250 \mathrm{K}.$

Solution

Verified
Step 1
1 of 3

In this exercise we have to find an expression for the change in entropy when two block of the same substance and of equal mass are brought into thermal contact and allowed to reach equilibrium

We have to evaluate change in entropy for two blocks of copper

We will calculate the final temperature by using:

Heat lost $=$ heat gained

\begin{align*} \mathrm{m}_{1}(500 \mathrm{K}-\mathrm{T})&=\mathrm{m}_{2}(\mathrm{T}-250 \mathrm{K})\\ 500_{\mathrm{g}}(500 \mathrm{K}-\mathrm{T})&=500_{\mathrm{g}}(\mathrm{T}-250 \mathrm{K})\\ 2 \mathrm{T}&=750\\ \mathrm{T}&=375 \mathrm{K}\\ \end{align*}

Firstly we will calculate $\Delta S_{C}$:

\begin{align*} \Delta S_{C}&=nC_{P,m} \ln \frac{T_{f}}{T_{i}}\\ &=\frac{500 \mathrm{g}}{63.55 \mathrm{g}\ \mathrm{mol}} \cdot 24.4 \mathrm{J}\ \mathrm{K}\ \mathrm{mol} \cdot \ln \left(\frac{375 \mathrm{K}}{250 \mathrm{K}}\right)\\ &=7.86 \mathrm{mol} \cdot 24.4 \mathrm{J}\ \mathrm{K}\ \mathrm{mol} \cdot(0.405)\\ \Delta S_{C}&=77.76 \mathrm{J}\ \mathrm{K}\\ \end{align*}

## Recommended textbook solutions #### Chemistry: The Molecular Nature of Matter and Change

7th EditionISBN: 9780073511177 (2 more)Patricia Amateis, Silberberg
6,032 solutions #### Chemistry: The Central Science

14th EditionISBN: 9780134414232 (9 more)Bruce Edward Bursten, Catherine J. Murphy, H. Eugene Lemay, Matthew E. Stoltzfus, Patrick Woodward, Theodore E. Brown
7,736 solutions #### Atkins' Physical Chemistry

11th EditionISBN: 9780198769866James Keeler, Julio de Paula, Peter Atkins
1,692 solutions #### Modern Chemistry

1st EditionISBN: 9780547586632 (2 more)Jerry L. Sarquis, Mickey Sarquis
2,184 solutions