Consider an ideal gas enclosed in a 1.00 L container at an internal pressure of 20.0 atm.

Question

Calculate the work, 𝑤 , if the gas expands against a constant external pressure of 1.00 atm to a final volume of 20.0 L.

Now calculate the work done if this process is carried out in two steps. 

1. First, let the gas expand against a constant external pressure of 2.00 atm to a volume of 10.0 L.
2. From the end point of step 1, let the gas expand to 20.0 L against a constant external pressure of 1.00 atm.

Answer 1

Pressure-volume work:

w = -P∆V

w = work

P = pressure in atm

∆V = change in volume in L

w = -(1 atm)(20.0 L)

w = - 20 L-atm x 101.325 J / L-atm = -2027 Joules

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step 1:

w = -2 atm x 10 L x 101.325 J/Latm = -2027 J

step 2:

w = -1 atm x 10 L x 101.325 J/Latm = -1013 J