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# Heat, Work, and Processes

## In-class Content

### Activity: Using $pV$ and $TS$ Plots

Link to Using $pV$ and $TS$ Plots Activity

**Activity Highlights**

- This small group activity is designed to help students learn to read $pV$ and $TS$ plots and to understand simple cyclic processes.
- Students work out the heat and work for each leg of a cycle, as well as the totals for the cycle.
- The wrap-up discussion highlights student difficulties with the sign of heat and work, and reinforces the concept of heat and work being path-independent.

## Homework for Energy and Entropy

- (HeatAndWork)
*What goes here?***Heat and work**FOr each of the following processes, solve for the heat or work done.A system expands from initial volume $V_0$ to final volume $V_f$. During the process the pressure is given by \[p=\frac{N k_b T}{V}\] where $k_B T$ and $N$ are constant. How much work does the system do on its environment?

A system is heated from initial entropy $S_0$ to final entropy $S_f$. During this process the temperature is held fixed. How much energy is transferred into the system by heating during this process?

A system is heated from initial entropy $S_0$ to final entropy $S_f$. During this process the temperature is given by \[T=T_0 + \frac{S-S_0}{C_V}\] where $T_0$ and $C_V$ are constants. How much energy is transferred into the system by heating during this process?

A system expands from initial volume $V_0$ to final volume $V_f$. During the process the pressure is given by \[p=p_0 \left( \frac{V_0}{V} \right) ^\gamma \] where $p_0$ is the initial pressure. How much work does the system do on its environment?