Average speed of particles in a Fermi gas.

See attached file.

Show that the fundamental thermodynamic relation implies that U is proportional to T^4 for a photon gas.

See attached file.

Heat conduction

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Expression for magnetic susceptibility of a magnetic solid is given. To determine the change in entropy with change in magnetic field at constant temperature.

Please refer attachment.

Knowledge of molecular speeds and of gravity.

Consider the atmosphere of the earth; and the moon. Using your knowledge of molecular speeds and of gravity, find the following and comment about your results, etc.. Calculate the escape velocity of a mass at the surface of the earth. The T of the earth's upper atmosphere is actually pretty high ; say 1000 K. Find the probability of a nitrogen molecule to this T moving faster than the escape velocity. You will need to use a computer ; otherwise clearly set - up and estimate your answer. Comment on your answer. Repeat for a hydrogen molecule and helium atom. And comment on the answers u get here.Find the moon's escape speed, and comment on the above results for the moon.