**Step 1. **V_{2} using Boyle's Law

${\mathbf{P}}_{\mathbf{1}}{\mathbf{V}}_{\mathbf{1}}\mathbf{=}{\mathbf{P}}_{\mathbf{2}}{\mathbf{V}}_{\mathbf{2}}\phantom{\rule{0ex}{0ex}}{\mathbf{V}}_{\mathbf{2}}\mathbf{=}\frac{{\mathbf{P}}_{\mathbf{1}}{\mathbf{V}}_{\mathbf{1}}}{{\mathbf{P}}_{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{V}}_{\mathbf{2}}\mathbf{=}\frac{(3.2\overline{)\mathrm{atm}})(21.0L)}{\mathbf{1}\mathbf{.}\mathbf{60}\mathbf{}\overline{)\mathbf{atm}}}$

A 21.0-L volume of an ideal gas in a cylinder with a piston is at a pressure of 3.2 atm. Enough weight is suddenly removed from the piston to lower the external pressure to 1.6 atm. The gas then expands at constant temperature until its pressure is 1.6 atm. Find q for this change in state.

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