Question

The pressure of a photon gas is P = 1/4αT³. Determine the free energy of the photon gas. Assume α is the constant.

a. F = - (3/4αVT²)
b. F = - (1/16αVT⁴)
c. F = - (3/4αT²)
d. F = - (1/4αVT³)

Answer 1

The free energy of a photon gas can be determined by integrating the equation for pressure with respect to temperature.

Step-by-step explanation:

The free energy of a photon gas can be determined by integrating the equation for pressure with respect to temperature. The equation for pressure is given as P = 1/4αT³, where α is the constant. The free energy, F, is given by the equation F = -∫P dT. Integrating the equation for pressure gives F = -1/12αT⁴. Therefore, the correct option is d. F = - (1/4αVT³).