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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?

Md Ariful Islam

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Md Ariful Islam

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

$w_"rev" = -P int_(V_1)^(V_2) dV$

$= -P (V_2 - V_1) = -"288 J"$

Since the gas did work, $V_2 > V_1$ and work should be negatively-signed. That is, $w_"rev" < 0$.

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

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

Therefore, to solve for $V_2$, we have:

$color(blue)(V_2) = -(w_"rev")/P + V_1$

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

$~~$ $color(blue)("1.67 L")$

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