Question

7. Do Problem 4.65E below. 4.65E The piston/cylinder shown in Fig. P4.12 contains carbon dioxide at 50 lbf/in.?, 200 F with a volume of 5 ft3. Mass is added at such a rate that the gas compresses according to the relation PV 1.2 = constant to a final temperature of 350 F. Determine the work done during the process. Ро CO2 8 FIGURE P4.12

Answer 1

Given data:

Initial pressure of carbon dioxide, P₁ = 50 lbf/in²

The initial temperature of carbon dioxide, T₁ =

200°F

The initial volume of the carbon dioxide, V₁ = 5 ft³

Gas compresses according to

PV 1.2 = constant

Final temperature, T₂ =

350°F

Solution:

The workdone for polytropic process is,

W P2V2 – P1V1 1-n n=1

Assuming an ideal gas,

PV mRT

mR= P1V1 T

convert pressure from psig to psia

P1 = 50+ 14.7 = 64.7 psia

convert temperature from
F
to
R

Ti = 200 + 460 = 660ºR

64.7 x 5 mR= 660

mR= 0.49 lbf-ft/'R

W mR(T2-T) 1-n n+1

Here,

n = 1.2

So,

W mR(T2 - T1) 1-n n+1

substituting respective values,

W 0.49(350 – 200) 1 - 1.2 W = -367.5 lbf-ft

Therefore, the workdone during the process is -367.5 lbf-ft.