Question

The specific heat capacity of a metal at low temperature (T) is given as Cp (kJ K-1kg-1) = 32(T/400)3. A 100 g vessel of this metal is to be cooled from 20 K to 4 K by a special refrigerator operating at room temperature (27°C). The amount of work required to cool the vessel is

(a) equal to 0.002 kJ

(b) greater than 0.148 kJ

(c) between 0.148 kJ and 0.028 kJ

(d) less than 0.028 kJ

Answer 1

Correct Option (c) between 0.148 kJ and 0.028 kJ

Explanation:

Heat required to change the temperature of vessel by a small amount dT,

Work done required to maintain the temperature of sink to T2,

As temperature is changing from 20 K to 4 K, work done required will be more than W1, but less than W2.