Question

The gas caused cooling in a refrigerator on expansion because:
A. The density of gas goes down
B. Heat of the gas is lost as work is done by the gas
C. Work done by the gas is converted into heat
D. The heat is spread over a large space

Answer 1

The entropy of a system is the measure of randomness of the molecules. The cooling and heating of a gas is basically the randomness and hence it is directly related to entropy.

Complete step by step answer:
The entropy of a system is
$\Delta S=\frac{{{q}_{rev}}}{T}$
$\Delta S>0$, randomness increases hence heat is absorbed.
$\Delta S<0$ , randomness decreases hence heat is released.
Now,
$Q=\Delta U+W$
In the given question the work is done by the gas as it expands and it is positive.
Also, heat or energy is lost since cooling is happening so it is not converted into heat.
Therefore, Q is positive.
In the question, due to cooling the temperature decreases.
Hence, the entropy is greater than one; this means randomness increases and heat is absorbed.

The correct option is B that is heat of the gas is lost as work is done by the gas.

Note: You can conclude you answer just by looking at the Q that is heat.
Also, we can see that the other options are incorrect as in
We have not given enough data to look for density as there is no mention of mass and volume.
C. The work done cannot be converted into heat as the system is cooling and temperature will increase if heat is released.
D. Again if heat spreading is there it will increase the temperature of the system which is not the case here.