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Please answer this question with explanation... The internal energy of an ideal gas is related as U=a+b(PV).( where P is pressure of gas and V is volume of gas , a and b are constants of appropriate dimensions.Then find the Y(gamma) value of gas. 1)a/b. 2)1+(b/a) 3)1 + (1/a). 4) 1+ (1/b)

 
Please answer this question with explanation...
 
The internal energy of an ideal gas is related as U=a+b(PV).( where P is pressure of gas and V is volume of gas , a and b are constants of appropriate dimensions.Then find the Y(gamma) value of gas.
1)a/b.      2)1+(b/a)    3)1 + (1/a).  4) 1+ (1/b)

Grade:12th pass

1 Answers

Vikas TU
14149 Points
5 years ago
 U=a+b(PV)
At constant volume,
C=(∂ U/∂ T)v
or
dU = Cv dT
dU = bP dV (at constant volume)
Thus, CvdT = bPdP
integrating both sides, we get
Cv * T = bP^2/2
or
Cv = bP^2/2T...............................(1)
At constant Pressure,
dU/dV = Cp = 0 + bP
and from
 
Cp =(∂ U/∂ T)p
or
dU = Cp dT
dU = 0 + bP
or
bVdv = Cp dT
integerating both sides we get,
b*V^2/2 = Cp*T
or
Cp = bV^2/2T...................(2)
From eqns. (1) and (2)
Y = Cp/Cv = (bV^2/2T)/(bP^2/2T)
   = bV^2/bP^2
   = (V/P)^2

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