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• Notes

$\begin{array}{l}{\text { A gas in a cylinder expands from a volume of } 0.110 \mathrm{m}^{3} \text { to }} \\ {0.320 \mathrm{m}^{3} . \text { Heat flows into the gas just rapidly enough to keep the }} \\ {\text { pressure constant at } 1.65 \times 10^{5} \text { Pa during the expansion. The total }} \\ {\text { heat added is } 1.15 \times 10^{5} \mathrm{J} \text { . (a) Find the work done by the gas. (b) }} \\ {\text { Find the change in internal energy of the gas. (c) Does it matter }} \\ {\text { whether the gas is ideal? Why or why not? }}\end{array}$

$Q=+1.15 * 10^{5} \mathrm{J}$

$w=p \cdot \Delta v=1.65 * 10^{5}*(0.32-0.11)=3.47 * 10^{4} \mathrm{J}$

$\Delta U=Q-W=1.15 * 10^{5}-3.47 * 10^{4}=8.04 * 10^{4} \mathrm{J}$

$w=p \cdot \Delta v$

$\Delta U=Q-W$

$\begin{array}{l}{\text { A gas in a cylinder is held at a constant pressure of }} \\ {1.80 \times 10^{5} \mathrm{Pa} \text { and is cooled and compressed from } 1.70 \mathrm{m}^{3} \text { to }} \\ {1.20 \mathrm{m}^{3} . \text { The internal energy of the gas decreases by } 1.40 \times 10^{5} \mathrm{J} \text { . }} \\ {\text { (a) Find the work done by the gas. (b) Find the absolute value }|Q| \text { of }} \\ {\text { the heat flow into or out of the gas, and state the direction of the heat }} \\ {\text { flow. (c) Does it matter whether the gas is ideal? Why or why not? }}\end{array}$

$W=\int_{v_{1}}^{v_{2}} P \cdot d v=p\left(v_{2}-v_{1}\right)$

$∴ W=\left(1.8 * 10^{5}\right)(1.2-1.7)=-9 * 10^{4} J$

$\Delta U=Q-W \quad \longrightarrow \quad Q=\Delta U+W$

$=-1.4 * 10^{5}+\left(-9 * 10^{4}\right)=-2.3 * 10^{5} J$

$\text { (out of the gas) }$

$\begin{array}{l}{\text { Boiling Water at High Pressure. When water is boiled }} \\ {\text { at a pressure of } 2.00 \text { atm, the heat of vaporization is }} \\ {2.20 \times 10^{6} \mathrm{J} / \mathrm{kg} \text { and the boiling point is } 120^{\circ} \mathrm{C} \text { . At this pressure, }} \\ {1.00 \mathrm{kg} \text { of water has a volume of } 1.00 \times 10^{-3} \mathrm{m}^{3}, \text { and } 1.00 \mathrm{kg} \text { of }} \\ {\text { steam has a volume of } 0.824 \mathrm{m}^{3} . \text { (a) Compute the work done when }} \\ {1.00 \mathrm{kg} \text { of steam is formed at this temperature. (b) Compute the }} \\ {\text { increase in internal energy of the water. }}\end{array}$

$Q=2.2 * 10^{6}>0 \quad(\text { into the water })$

$P=2 \ atm=2.03 * 10^{5} \ \mathrm{Pa}$

$W=P \ \Delta V=\left(2.03 * 10^{5}\right)\left(0.824-1*10^{-3}\right)=1.67 * 10^{5} J$

$\Delta U=Q-W=2.2 * 10^{6}-1.67 * 10^{5}=2.03 * 10^{6} J$

$\begin{array}{l}{\text { An ideal gas is taken }} \\ {\text { from } a \text { to } b \text { on the } p V \text { -diagram }} \\ {\text { shown in Fig. } \mathrm{E} 19.15 . \text { During }} \\ {\text { this process, } 700 \mathrm{J} \text { of heat is }} \\ {\text { added and the pressure dou- }} \\ {\text { bles. (a) How much work is }} \\ {\text { done by or on the gas? Explain. }} \\ {\text { (b) How does the tempare to its }} \\ {\text { temperature at } b ? \text { Empare to its }} \\ {\text { energy of the gas at } a \text { compare }} \\ {\text { to the internal energy at } b ?} \\ {\text { Again, be specific and explain. }}\end{array}$ $\Delta v=0 \quad Q=+700 \mathrm{J}$

$w=0$

$p V=m R t$

$\frac{P}{T}=\frac{n R}{V}=\text { comstant }$

$T_{b}=2 T_{a}$

$∵ W=0 \quad \Delta u=Q-W \rightarrow \Delta U=Q=+700 \mathrm{J}$

$U_{b}=U_{a}+700$