Question

The relation between internal energy U, pressure P and volume V of a gas in a process is U = a + bPV, where a and b are positive
constants. What is the value of y?
(A)
(B) 5+1
b
(C)
b.
(D)​

Answer 1

Answer:

here is your answer

hope it help u

Explanation:

In an adiabatic process no heat is exchange.   i.e. (dQ=0)

dQ=dU+PdV

0=dU+PdV

d(a+bPV)+PdV=0 ... (V=a+bPV..(given))

bPdV+bVdP+PdV=0

(b+1)PdV+bVdP=0

(b+1)(dV/V)+b(dP/P)=0 ... (dividing both by PV)

Integrating we get,

(b+1)logV+b(logP)= constant

logV  

(b+1)

+logP  

b

= constant

V  

(b+1)

×P  

b

= constant

Multiply power by  

b

1

​  

 

PV  

((b+1)/b)

=constant=PV  

γ

 

γ=  

b

b+1

​  

 

Answer 2

Answer:

The answer is a option B