A small water droplet of diameter D = 100 μm and temperature Tmp = 0°C falls on a nonwetting metal surface that is at temperature Ts = −15°C. Determine how long it will take for the droplet to freeze completely. The latent heat of fusion is hsf = 334 kJ/kg. Hint: consider what will be true of the water droplet temperature given its initial temperature.

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.