Find an equation for the work of reversible, isothermal compression of 1 mol of gas in a piston/cylinder assembly if the molar volume of the gas is given by where b and R are positive constants.

Question

What will be an ideal response?

Answer 1

The work of a reversible expansion or compression is given by



where the integral is over the path from the initial to final state. If the temperature is fixed and the pressure and volume are related by



Then we can substitute P in terms of V or dV in terms of P into the integral (depending whether we want to specify the limits of the integral in terms of P or V). If we want substitute for dV in terms of P, we have to differentiate the

relationship between V and P, to get



Substituting this into the integral for the work, we have



Taking the alternative approach, we could substitute for P in terms of V, writing



Substitution for and in terms of and shows that this result is identical to the first one.