April 4, 2017

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26 Isochoric Cooling and Isobaric Expansion (Moscow Phys-Tech) An ideal gas of total mass and molecular weight is isochorically (at constant volume) cooled to a pressure times smaller than the initial pressure The gas is then expanded at constant pressure so that in the final state the temperature coincides with the initial temperature Calculate the work done by the gas. 27 Venting (Moscow Phys-Tech) A thermally insulated chamber is pumped down to a very low pressure. At some point, the chamber is vented so that it is filled with air up to atmospheric pressure, whereupon the valve is closed.

In a spin-1/2 Fermi gas is given at is the mass of the gas particles, and by is the number a) Show that where is the chemical potential. b) Calculate the sound velocity in the limit of zero temperature. Express your answer in terms of c) Show that in a Bose gas below the Bose–Einstein temperature. 70 Bose Condensation Critical Parameters (MIT) Consider an ideal Bose gas of N particles of mass and spin zero in a volume V and temperature above the condensation point. a) What is the critical volume below which Bose–Einstein condensation occurs?

31). and are adiabatic compression and expansion, respectively; and are constant-volume processes. 32 and atm. 32). Assume that the heat capacities of the gas and are constant. 33). Assume and are constant. 34 shows container A of variable volume V controlled by a frictionless piston, immersed in a bath at temperature This container is connected by a pipe with a porous plug to another container, B, of fixed volume Container A is initially occupied by an ideal gas at pressure P while container B is initially evacuated.

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