8. Thermodynamics can be applied to a wide variety of systems; we’ve done severa

Question

8. Thermodynamics can be applied to a wide variety of systems; we’ve done several in class.

Consider blackbody radiation. If the walls of any “empty” vessel are maintained at a constant temperature T it is found that the vessel is a repository of electromagnetic information. Regardless of the quantum nature of this system, thermodynamic theory is still applicable.

The system is characterized by two equations. One is P = U/3V and the other is the Stefan-Boltzmann Law, U = bVT4, where b is a constant.

Note that these equations of state are functions of U and V, but not N. This is because the cavity is “empty” and there are no “particles” from a macroscopic perspective. Hence, the system is governed by a fundamental equation that has only two independent extensive variables, S = S(U,V). So, for this system, the two equations of state constitute a complete set. Write the equations of state in the proper form and find the fundamental relation for this system.

Explanation / Answer

given for a blackbody
P = U/3V

and the stefan's boltzmann law
U = b*VT^4

combinig tghese two equations
P = b v T^4 / 3V
P = b T^4
here P is radiant power per unit area, b is stefans constant with the value of 5.67*10^-8, and T is absolute temperature

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