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