calculating work

Question

Consider an ideal gas enclosed in a 1.00 L container at an internal pressure of 24.0 atm. 

Calculate the work, 𝑤, if the gas expands against a constant external pressure of 1.00 atm to a final volume of 24.0 L.

𝑤= __________ J



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 1.50 atm to a volume of 16.0 L.
2. From the end point of step 1, let the gas expand to 24.0 L against a constant external pressure of 1.00 atm.

Answer 1

w = -P∆V

w = work = ?

P = pressure = 1.00 atm

∆V = change in volume = 24.0 L - 1.00 L = 23 L

w = -(1.00 atm)(23 L) = -23 Latm

w = -23.0 Latm x 101.325 J / Latm

w = -2330 J (negative since system is doing work on the surroundings)

w = -(1.5 atm)(15 L) = -22.5 Latm

w = -(1.00 atm)(8 L) = -8 Latm

w = -22.5 + -8 = -30.5 Latm

w = -30.5 Latm x 101.325 J / Latm

w = -3090 J