A system consists of N very weakly interacting particles at a temperature T sufficiently high so that classical statistical mechanics is applicable. Each particle has a mass m and is free to perform one-dimensional oscillations about its equilibrium position. Calculate the heat capacity of this system of particles at this temperature in each of the following cases:

In the winter, in order to keep the classroom steadily at 68 f before 10 pm, heating with an average rate of 42,000 btu/hr is provided. assume the outdoor temperature maintains at 32°f, determine the electrical power (kw) required to (a) operate a reversible heat pump (b) operate a real heat pump with a cop (7) of 4.5 and (c) operate an electrical-resistance heater.

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Along steel shaft of 10 cm diameter is austenised at 870°c and then quenched in a liquid at 30oc. the average surface heat transfer coefficient is 2000 w/m2. °c. the relevant thermophysical properties of the shaft are: p=7800 kg/m", k=20 w/mk, cp=0.46 kj/kg.k calculate: a)-the time required for the center temperature to drop to 200°c. b)-the temperature at half-radius at that moment. c)-the amount of heat that had been transferred to the liquid by that time per meter length of the shaft