Question

Derive the expression for the work done by gaseous system of isothermal expansion of an ideal gas.

Answer 1

w= -$\int\limits^v_u {P} \, dV$
Where u,v are initial and final volumes, for the expansion

using ideal gas equation,
pV=nRT
p=(nRT/V)

-w=  $\int\limits^u_v {(nRT/V)} \, dV$

Hence, for an isothermal process,temperature is constant.The work done can be expressed as,
W=-nRT㏑(v/u)