A cylinder with a moving piston expands from an initial volume of 0.250 L against an external pressure of 2.00 atm. The expansion does 288 J of work on the surroundings. What is the final volume of the cylinder?

Jul 10, 2016

This is asking you to apply the definition of reversible work:

${w}_{\text{rev}} = - P {\int}_{{V}_{1}}^{{V}_{2}} \mathrm{dV}$

$= - P \left({V}_{2} - {V}_{1}\right) = - \text{288 J}$

Since the gas did work, ${V}_{2} > {V}_{1}$ and work should be negatively-signed. That is, ${w}_{\text{rev}} < 0$.

Note that your pressure is in $\text{atm}$, but your energy is in $\text{J}$. A convenient conversion unit using the universal gas constants $R = \text{8.314472 J/mol"cdot"K}$ and $R = \text{0.082057 L"cdot"atm/mol"cdot"K}$ to convert from $\text{J}$ to $\text{L"cdot"atm}$ is:

("0.082057 L"cdot"atm")/"8.314472 J"

Therefore, to solve for ${V}_{2}$, we have:

$\textcolor{b l u e}{{V}_{2}} = - \frac{{w}_{\text{rev}}}{P} + {V}_{1}$

= -(-"288" cancel("J") xx ("0.082057 L"cdotcancel("atm"))/("8.314472" cancel("J")))/("2.00" cancel("atm")) + "0.250 L"

$\approx$ $\textcolor{b l u e}{\text{1.67 L}}$