Question

Prove that for finite change in vvolume In (V2/V1) = alpha (T2-T1)
​

Answer 1

Answer:

dT = 0 so dU = and dH =

q = –w

w = – nRT ln 









V2

V1

P2V2 = P1 V1 or

V2

V1

=

P1

P2

w = – nRT ln









P1

P2

Adiabatic Reversible Expansion

ñq = so dU = ñw = – P dV

dU = – P dV or dU = Cv dT

Cv dT = – P dV

Cv

dT

T

= – nR

dV

V

⌡



⌠

T1

T2Cv

dT

T

= – ⌡



⌠

V1

V2

nR

dV

V

Cv ln T |

T2

T1

= – nR ln V |

V2

V1

Cv ln









T2

T1

= – nR ln









V2

V1

Method 1:

Cv

nR ln









T2

T1

= – ln









V2

V1

c = Cv/nR











T2

T1

Cv/nR

= 









V1

V2

or V2T

Cv/nR

2

= V1T

Cv/nR