Answer to Question #165477 in Mechanical Engineering for Rodel

Question #165477

Ammola vapor is compressed in a closed system from 15 psia, 3 cu ft, to 150 psia, 0.4 cu ft. according to the relation pVn = constant. Assumin the vapor to be an ideal gas with the gas constant as 90.72 lbm-ft/lbf -°R and cv = 0.384 BTU/lbm - °R compute the heat transferred and the work.


1
Expert's answer
2021-02-22T07:31:39-0500

As per the relation

"PV^n= C, P_1V_1^n=P_2V_2^n"

"15\\times 3^n= 150\\times 0.4^n"

"(\\frac{3}{0.4})^n=10"

take log both sides

"nlog(7.5)= log(10)"

0.875n=1

n=1.14

so here value of n which follows above equation is 1.14

Now, we know that work done for polytropic process is

"W=\\frac{P_1V_1-P_2V_2}{n-1}=-107.14"

from ideal gas equation we can find value of temperature as

"PV=nRT, T_1=\\frac{P_1V_1}{nR}=\\frac{15 \\times 3}{1\\times 90.72}" =496 K,"T_2= \\frac{P_2V_2}{nR}=661.37 K"

"\\Delta U= n C_vdT=1\\times 0.384\\times 165.37=62.508 ft-lb_f"

Heat transfer as per first law of thermodynamics

"\\Delta Q= \\Delta U + \\Delta W"

"\\Delta Q=-43.63 ft lb_f"


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Comments

Assignment Expert
26.02.21, 15:00

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Rodel
23.02.21, 03:10

THANK YOU SO MUCH

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