Question

You have 1.25 mol of hydrogen gas (CV = 5R/2 and Cp= 7R/2) at absolute temperature 325 K. You allow the gas to expand adiabatically to a final temperature of 195 K.

1) How much work does the gas do while being compressed?

2) What is the ratio of its final volume to its initial volume?

3) What is the ratio of the final gas pressure to the initial gas pressure?

Answer 1

Solution:

From the information given,

= C_p/C_v = 7/5

a)

For a adiabatic process, Q = 0

U + W = 0

W = -U

= - nC_vT

= - 1.25 *[5/2]*8.314*[195 - 325]

= 3378 J.

b) TV^-1 = constant

V₂/V₁ = [T₁/T₂]^{1/ -1}

= [325/195]^1/[7/5-1]

= [325/195]^5/2

= 3.586 .

C) PV= const

P₂/P₁ = [V₂/V₁]^-7/5

= 3.586^-7/5

= 0.1673

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