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Assume that all the molecules are in the electronic ground state with degeneracy At what temperature is this approximation valid? 40 Gas in Harmonic Well (Boston) A classical system of N distinguishable noninteracting particles of mass is placed in a three-dimensional harmonic well: a) Find the partition function and the Helmholtz free energy. b) Regarding V as an external parameter, find the thermodynamic force conjugate to this parameter, exerted by the system; find the equation of state and compare it to that of a gas in a container with rigid walls.

24 15 Spring Cylinder (Moscow Phys-Tech) One part of a cylinder is filled with one mole of a monatomic ideal gas at a pressure of 1 atm and temperature of 300 K. A massless piston separates the gas from the other section of the cylinder which is evacuated but has a spring at equilibrium extension attached to it and to the opposite wall of the cylinder. 24). After reaching equilibrium, the volume occupied by the gas is double the original. Neglecting the thermal capacities of the cylinder, piston, and spring, find the temperature and pressure of the gas.

C) Using the observations and the result of part (a), estimate this lower limit (in units of and comment on whether current measurements of neutrino masses allow Draco to be held together in the manner suggested. 80 39 Einstein Coefficients (Stony Brook) You have two-state atoms in a thermal radiation field at temperature T. The following three processes take place: 1) Atoms can be promoted from state 1 to state 2 by absorption of a photon according to 2) Atoms can decay from state 2 to state 1 by spontaneous emission according to 3) Atoms can decay from state 2 to state 1 by stimulated emission according to The populations density is and are in thermal equilibrium, and the radiation a) What is the ratio b) Calculate the ratios of coefficients and c) From the ratio of stimulated to spontaneous emission, how does the pump power scale with wavelength when you try to make shortwavelength lasers?

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