Question

A perfect gas occupying a volume of 200 dm3 at 2 atm is isothermally compressed at 500K with a piston actuated at external pressure, Pext, constant. Q3a) What will be the smallest value of Pext for a final volume of 50 dm3? Q3b) Calculate the work, w, done with this value of Pext. Is this a reversible or irreversible work? Q3c) This same gas is then compressed isothermally and reversibly at 500K V1 = 200 dm3 at V2 = 50 dm3. Calculate for this transformation the ΔU, wrev and qrev.

Answer 1

V1= 200 dm³

P1= 2 atm

T1= 500K

Pext constant

V2 = 50 dm³

Pext = ?

PV = nRT

2atm x 200 dm³ = n x 8.314 x 500

n = 0.096

a) when the external pressure is constant , the system is compressed or expanded by the atmosphere, which exerts same pressure through out.

AS pressure is consstant , so the minimum external pressure on compressing from volume 200 dm³ to 50 dm³ will be zero.

Pext = 0

b) work done = - Pext

work done = - Pext (V2- V1)

work done =- 0 ( 50 - 200)

work done = 0

work done in this case is reversible.

c)for isothermal reversiby compression

W =- nRT ln V2/ V1

W= 0.096 x 8.314 x 500 ln 50 / 200

W =8.314 x 500 x-1.386

W = 553.113 kj

change in energy of the system for the isothermal process is zero

and since the temperature is constant, ΔT=0 and ΔU=0. Using the first law of thermodynamics

and we have q = -W

q rev =- 553.113 KJ

The heat added to the system is negative because the gas is compressed.