Question

How will you prove that work done in an isothermal process is always greater than adiabatic process?

Answer 1

Hint: If an ideal gas is compressed depending on the parameters such as temperature, pressure and volume. Due to compression, work is done on the gas either adiabatically or isothermally.

Complete answer:
Adiabatic process is the process in which there is change in pressure, volume and temperature without exchange of heat within the surrounding and system.
Isothermal process is the process in which there is change in pressure and volume at constant temperature.
In adiabatic processes, there is no exchange of heat which means there is no change in the internal energy hence no work is done. This isn’t the same as an isothermal process.
The work done by the gas can be represented by PV diagram:

The work done by the gas during the expansion is the area under the curve of the PV diagram. As we see in the following diagram,

As we can see here, the isothermal expansion is less steep compared to the adiabatic expansion. This is one of the results.
Through the diagram, it clearly seems that the area under the isothermal process curve is greater than the area under the adiabatic curve.
Thus, this results leads to the conclusion that the work done by the isothermal process is greater compared to adiabatic process.

Note:
In case of an ideal gas, there are three processes which take place viz. Isothermal, Adiabatic and Isochoric process. Among which, adiabatic expansion is different since pressure, volume and temperature changes at same time. In a graph, if the line is steeper that means the flow rate is higher.