Question

Question: An ideal gas undergoes an isobaric compression and then an isovolumetric process that brings it back to its initial temperature. Had the gas undergone one isothermal process instead,

(a) the work done on the gas would be the same.

(b) the work done on the gas would be less.

(c) the work done on the gas would be greater.

(d) Need to know the temperature of the isothermal process.

Short answer

The work done on the gas would be greater.

Step-by-step solution

Understanding of isovolumetric process 

The isovolumetric process may be defined as the thermodynamic process that occurs at constant volume. The work done in this process is equivalent to zero.

Pressure volume curve of an ideal gas 

The PV curve of an ideal gas is shown below.

In the PV diagram, the line DA represents the isovolumetric process, the line DB represents the isobaric process, and the line AB represents the isothermal process.

The area under the curve AB is equal to the work done in the isothermal process. The AB curve area represents an isothermal process, which covers all the area under the curved line. This area is the sum of the area under the DB line and the area under the AD line. Thus, the work done in the isothermal process is more.

Therefore, option (c) is the correct answer