Question

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

Answer 1

Consider one gram mole of an ideal gas enclosed in a cylinder with perfectly conducting walls and fitted with a perfectly frictionless and cobducting piston .
Let P1, V1 , T be the initial pressure , volume and temperature of the gas .
Let the gas expand to volume V2 , when pressure reduced to P2 and temperature remains constant T . At any instant during expansion , let the pressure of the gas be P.

If A is the area of the cross section of the piston , then force exerted by the gas on the piston is F = P x A
If we assume that pressure of the gas during an infinitestimally small outward displacement dx of the piston remain constant , then small amount of work done during expansion
dW = F x dx
= P x A x dx
dW = P ( d V )

Total work done by the gas in expansion from initial volume V1 to final volume V2 is W = P ( d V )

see the derivation in pic : )
W = RT log10 V2 / V1
W = 2.303 R T log 10 V2 / V1
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