The specific heat capacity of a metal at low temperautre

Question:

The specific heat capacity of a metal at low temperautre $(T)$ is given as $C_{p}\left(k J J k^{-1} k g^{-1}\right)=32\left(\frac{T}{400}\right)^{3}$

A 100 gram vessel of this metal is to be cooled from $20^{\circ} \mathrm{K}$ to $4^{\circ} \mathrm{K}$ by a special refrigerator operating at room temperature $\left(27^{\circ} \mathrm{C}\right)$. The amount of work required to cool the vessel is:-

 

  1. equal to $0.002 \mathrm{~kJ}$

  2. greater than $0.148 \mathrm{~kJ}$

  3. between $0.148 \mathrm{~kJ}$ and $0.028 \mathrm{~kJ}$

  4. less than $0.028 \mathrm{~kJ}$


Correct Option: , 3

Solution:

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