Question

what is isothermal process . Derive an expression for the work done during isothermal process

Answer 1

Isothermal process : the process in which temperature will be always constant.
It is very process.

We know, A/C to 1st law of thermodynamics ,
∆Q = ∆U + W
If temperature is constant. ∴ ∆U = 0 { because intenral energy depends upon temperature e.g ∆U = nR∆T ∵ ∆T = 0 so, ∆U = 0 }
so,
∆Q = W
It means in isothermal process , heat supplied to body or heat released from body is equal to work done .

now,
we also know,
W = P∆V or PdV
W = PdV
∵ PV = nRT
P = nRT/V

W = (nRT/V)dV
= nRT∫dv/v
= nRTln[vf/vi]

Hence,
W = nRTln[Vf/Vi]