Work out isothermal process instantly with clear inputs, formula shown and shareable results.
In an isothermal expansion the internal energy of an ideal gas does not change, so every joule of work done comes from heat absorbed: W = nRT ln(V2/V1). One mole tripling its volume at 300 K does 2741 J of work and takes in exactly that much heat, gaining 9.13 J/K of entropy while the surroundings lose the same.
Isothermal work
W = n R T ln(V2 / V1)
Energy balance
dU = 0, so Q = W
Because internal energy depends only on temperature for an ideal gas. Hold temperature fixed and the first law reduces to Q = W.
Slowly, in good thermal contact with a reservoir. Fast changes are closer to adiabatic because heat has no time to flow.