Question

The relation between p,n and u is

Answer 1

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

Hence option b is correct