Question

derive the expression for PV work​

Answer 1

Explanation:

dW=−PdV

∴ Total work done when the gas expands from initial volume V

1

to the final volume V

2

, will be-

W=−∫

V

1

V

2

PdV

For an ideal gas,

PV=nRT

⇒P=

V

nRT

Therefore,

W=−∫

V

1

V

2

V

nRT

dV

For isothermal expansion, T is constant.

Therefore,

W=−nRT∫

V

1

V

2

V

dV

⇒W=−nRT[lnV]

V

1

V

2

⇒W=−nRT(lnV

2

−lnV

1

)

⇒W=−nRTln(

V

1

V

2

)

⇒W=−2.303nRTlog(

V

1

V

2

).....(1)

At constant temperature,

P

1

V

1

=P

2

V

2

⇒

V

1

V

2

=

P

2

P

1

Therefore,

W=−2.303nRTlog(

P

2

P

1

).....(2)