Question

Short answer

(a) In adiabatic process, the entropy will stay the same and (b) in isothermal process, the entropy will increase.

Step-by-step solution

Understanding adiabatic and isothermal process 

In the adiabatic process, the rate of heat transfer is equivalent to zero. On the other hand, in isothermal process the system temperature is always constant.

Explanation of change in entropy in adiabatic process 

When a certain gas expands adiabatically the heat transfer is equal to zero that is \(Q = 0\).

The relation of change in entropy is given by,

\(\Delta S = \frac{Q}{T}\)

Here, \(\Delta S\) is the change in entropy and T is the temperature.

On plugging the values in the above relation.

\(\begin{array}{l}\Delta S = \frac{0}{T}\\\Delta S = 0\end{array}\)

Thus, there will be no change in entropy that is \(\Delta S = 0\).

Explanation of change in entropy in isothermal process 

When a gas expands isothermally, the variation in its internal energy becomes zero. Also, the gas has to perform work on its surrounding. Hence, due to work done, there will be heat flow into the gas. The entropy of the gas relies on the heat flow so that the entropy will increase in this case.

Thus, there will be increase in entropy.