Consider a ruby crystal with two energy levels separated by an energy difference corresponding to a free-space wavelength lambda_0 = 694.3nm, with a Lorentzian lineshape of width Delta v = 330GHz. The spontaneous lifetime is t_sp = 3ms and the refractive index of ruby is n=1.76. What value should the population difference N be to achieve a gain coefficient gamma(v_0) = 0.5 cm^-1 ? How long should the crystal be to provide an overall gain of 4 at the central frequency when gamma(v_0) = 0.5 cm^-1 ? The gain coefficient at central wavelength for Lorentzian lineshape is given as: gamma (v_0) = N(lambda_0/2 pi n)^2 middot 1/t_sp Delta v

The density of a liquid could be found by using

As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. the first student rides 1100 m due east and then turns due north and travels another 1430 m before arriving at the destination. the second student heads due north for 1930 m and then turns and heads directly toward the destination. at the turning point, how far is the second student from the destination?