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?

1 Answer
Jul 10, 2016

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")