Answer
$1.6\times 10^{5}\ Pa$
Work Step by Step
Boyle's Law: If the gas with a fixed number of molecules has constant temperature, then
$\mathrm{P}_{\mathrm{i}}\mathrm{V}_{\mathrm{i}}=\mathrm{P}_{\mathrm{f}}\mathrm{V}_{\mathrm{f}}\qquad(17-7)$
The volume of a cylinder with base radius r and height h is
$\mathrm{V}= \pi r^{2}h$
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Solve 17-7 for $\mathrm{P}_{\mathrm{f}}.$
$P_{\mathrm{f}}=\displaystyle \frac{\mathrm{P}_{\mathrm{i}}\mathrm{V}_{\mathrm{i}}}{\mathrm{V}_{\mathrm{f}}}=\frac{\mathrm{P}_{\mathrm{i}}\pi r^{2}h_{\mathrm{i}}}{\pi r^{2}h_{\mathrm{f}}}=\frac{P_{\mathrm{i}}h_{1}}{h_{\mathrm{f}}}$
$=\displaystyle \frac{(137 \times 10^{3}\ \mathrm{P}\mathrm{a})(23.4\ \mathrm{c}\mathrm{m} )}{20.0\ \mathrm{c}\mathrm{m}}=1.6\times 10^{5}$ Pa
