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The relation between internal energy, pressure and volume of a gas in an adiabatic process is U=a+bPV.where a and b are positive constant. Then what will be value of gamma?i.e cp/cv ratio. A-a/b,B-b+1/b,D-a+1/a,c-b/a

Asked by Priyanka 7th November 2017, 2:41 PM
Answered by Expert
Answer:
In an adiabatic process, No heat is exchanged
dQ=dU+PdV
0=dU+PdV
 d(a+bPV)+PdV=0
bPdV+bVdP+PdV=0
(b+1)PdV+bVdP=0
(b+1)(dV/V) +b(dP/P) = 0
 
Integrating we get
(b+1)logV +b(logP)=constant
 
 
logV(b+1) +logPb=constant
log (V(b+1)xPb)= constant
V(b+1)xPb=constant
divide by 
Vb and p(b-1) on both sides
 
PV((b+1)/b)= constant=PVr
 
r=((b+1)/b)
 
Option B
Answered by Expert 6th December 2017, 3:05 PM
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