Question

Derive an expression of work done in isothermal non spontaneous process​

Answer 1

Answer:

Suppose 1 mole of gas is enclosed in isothermal container. Let P

1

,V

1

,T be initial pressure, volumes and temperature. Let expand to volume V

2

& pressure reduces to P

2

& temperature remain constant. Then, work done is given by

W=∫dW

W=∫

V

1

V

2

PdV

as PV=RT (n= mole)

P=

V

RT

W=∫

V

1

V

2

V

RT

dV

W=RT∫

V

1

V

2

V

dV

=RT[InV]

V

1

V

2

=RT[InV

2

−InV

1

]

W=RTIn

V

1

V

2

W=2.303RTlog

10

V

1

V

2

for constant temperature

P

2

P

1

=

V

1

V

2

So, also

W=2.303.RTlog

10

P

2

P

1