Question: Problem 2.4. A Carnot engine uses a paramagnetic substance as its working substance. The equation of state is M = (nDH/T), where M is the

Problem 2.4. A Carnot engine uses a paramagnetic substance as its working substance. The equation of state is M = (nDH/T), where M is the magnetization, H is the magnetic field, n is the number of moles, D is a constant determined by the type of substance, and T is the temperature.

(a) Show that the internal energy U, and therefore the heat capacity CM, can only depend on the temperature and not the magnetization. Let us assume that CM = C = constant.

(b) Sketch a typical Carnot cycle in the M-H plane.

(c) Compute the total heat absorbed and the total work done by the Carnot engine.

(d) Compute the efficiency of the Carnot engine.

P adiabatic Pi Pa Pa V V 2 3

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