Question

Prove that two reversible adiabatic paths can never cross. Assume that the

energy of the system under consideration is a function of temperature only.

(Hint: Suppose that two such paths can intersect, and complete a cycle with

the two paths plus one isothermal path. Consider the changes accompanying

each stage of the cycle and show that they conflict with the Kelvin statement

of the Second Law.)

Answer 1

Assume any two adiabatic path XY and XZ . These two paths intersects at X . Now we need to draw one isothermal path which intersects XY and XZ at the points Y and Z . This forms a reversible cycle. During the path XY and XZ , there is no heat transfer . Heat transfer takes place only in reversible isothermal path . This means that this cycle is exchanging heat with the surroundings at just one temperature . This violates Kelvin Planks second law