The COP of a refrigerator decreases as the temperature of th

The COP of a refrigerator decreases as the temperature of the refrigerated space is decreased. That is, removing heat from a medium at a very low temperature will require a large work input. Determine the minimum work input required in units of kJ to remove 1 kJ of heat from liquid helium at 3 K when the outside temperature is 300 K.

Solution

T_L=3k

T_H=300k

cop = T_L/(T_H-T_L)

        = 3/(300-3)

        = 0.0101

cop = Refregeration effect/work input

    0.0101 = 1/work input

work input = 1/0.0101

                  = 99kJ

from this example

   yes, removing heat from medium at a very low temperature requires large work and cop also decreses drastically