Consider the startup of a refrigerator. Initially, the contents are at the same temperature as the surroundings: TC0 = TH where TH is the (constant) surroundings temperature. With the passage of time, owing to work input, the contents temperature is reduced from to its design value TC. Modeling the process as a Carnot refrigerator operating between an infinite hot reservoir and a finite cold reservoir of total heat capacity Ct, determine an expression for the minimum work required to decrease the contents temperature from TC0, to TC.