Question

An ideal gas initially at P = 175 torr and V = 2.00 dm3 is allowed to expand against an external pressur of 122 torr until the pressures are equal. What is the work done by this process? What would be the work done if the gas expanded to the same final volume under an external pressure of 175 torr and was then allowed to relax at constant volume to the final pressure of 122 torr?

Answer 1

1.
Pi = 175 torr = 175/760 atm = 0.23 atm
Pf = 122 torr = 122/760 atm = 0.16 atm
Vi =2 dm^2 = 2 L
Vf= ?

UsE:
Pi*Vi =Pf*Vf
0.23*2 = 0.16*Vf
Vf = 2.875 L

W = - P*(Vf-Vi)
      = -0.16 atm (2.875 L - 2 L)
      = -0.14 atm-L
      = -0.14 * 101.3 J
      = -14.2 J
Answer: -14.2 J

2.
In the 2nd part as the volume is not chnaging work done is Zero
W = - Pi*(Vf-Vi)
      = -0.23 atm (2.875 L - 2 L)
      = -0.20 atm-L
      = -0.20 * 101.3 J
      = -20.3 J
Answer: 20.3 J