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
Truong-Son N.
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")#

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