Question

A gas is allowed to expand isobarically from .65 m3 to 1.70 m3. There are 39 moles of the gas at a pressure of 240 kPa. Assume the gas is monatomic ideal.

a. Sketch a PV diagram.

b. How much work was done by the gas during the expansion?

c. What were the initial and final temperatures of the gas?

d. Determine the change in the internal energy of the gas and the heat added to the gas?

Answer 1

Isobaric process

initial volume, V₁= 0.65 m³

final volume, V₂= 1.73 m³

no. of moles, n = 39

pressure,P = 240 kPa

a. PV diagram

b. Work done

W = PV

W = P(V2 - V1)

W = 240 x 1000 x (1.73-0.65)

W = 2.592 x 10⁵ J

c. Temperatures

We kniow, PV = nRT

T = (PV)/nR

initial temperature

T₁ = (240000 x 0.65)/(39 x 8.3145)

T₁ = 486.94 K

final temperature

T₂ = (240000 x 1.73)/(39 x 8.3145)

T₂ = 1280.43 K

d. change in internal energy

U = (3/2)NkT

       = 1.5 x 39 x 1.38 x 10^-23 x (1280.43 - 486.94)

       = 6.4 x 10^-19 J