Section A
Q1.
(a) Derive a general expression for the change in entropy of a real gas obeying the van der Waals equation.
(b) The boiling point of water at the top of a hill is found to be 90\circC, whereas it boils at 99.6\circC with the latent heat of evaporation of 2256.94 kJ/kg at the foot of the hill (where the pressure is 101.325 kPa). Assuming that the atmosphere is locally isothermal at 300 K (i.e. pv = p_0v0 is valid), estimate the height of the hill.
(c) A house, that is losing heat at a rate of 50,000 kJ/h when the outside temperature drops to 4°C, is to be heated by electric resistance heaters. If the house is to be maintained at 25°C at all times, determine the reversible work input for this process and the irreversibility.
(d) Determine the heat transfer rate from a rectangular fin of length 20 cm, width 40 cm and thickness 2 cm. The tip of the fin is not insulated and the fin has a thermal conductivity of 150 W/mK. The base temperature is 100°C and the fluid is at 20°C. The heat transfer coefficient between the fin and the fluid is 30 W/m^2K.
(e) What purposes does an expansion device serve in a vapour compression refrigeration system? Explain how a simple capillary tube can serve these purposes.