Section 15.9: Change of Variables in Multiple Integrals

An important problem in thermodynamics is to find the work done by an ideal Carnot engine. A cycle consists of alternating expansion and compression of gas in a piston. The work done by the engine is equal to the area of the region R enclosed by two isothermal curves \(xy=a, xy=b\) and two adiabatic curves \(xy^{1.4}=c, xy^{1.4}=d\), where \(0 < a < b\) and \(0 < c < d\). Compute the work done by determining the area of R.