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# Which of the following is the correct relation, if $W_1, W_2, W_3$, and $W_4$ are work done in isothermal, adiabatic, isobaric and isochoric reversible expansion for an ideal gas, thenA. ${W_3} > {W_1}$B. ${W_1} > {W_2}$C. ${W_2} > {W_4}$D. ${W_4} > {W_2}$

Last updated date: 14th Sep 2024
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Hint: As per thermodynamics, work is said to be done by the system when it transfers its energy to its surroundings. For the case of gas, work done is said to be done when a gas is compressed or is expanded.

Complete step by step answer:
As for the case of gas, there exists a change in the volume in case of expansion or contraction, and also there is a pressure experienced and hence it is also known as pressure-volume work. Gasses follow the below convention for the work done:
$work = - P\Delta V$
Here $\Delta V$ is the change in volume and P is the pressure
As per the thermodynamic process, a process is said to be isothermal if the change in temperature remains constant. Also for the case of an ideal gas, it is zero. In the case of an adiabatic process, energy is transferred to the system only in the form of work done, and no heat is transferred from the system to its surroundings. In the case of an isobaric process, the pressure or the force exerted by the molecules is constant. The isochoric process, also known as the isovolumetric process is a process in which the volume of the system remains constant. As per the given question, the isothermal process represented by ${W_1}$, an adiabatic process is represented by ${W_2}$, the isobaric process is represented by ${W_3}$ and an isochoric process is represented by ${W_4}$. The relationship between the work done in these four thermodynamic processes is given as

${W_3} > {W_1} > {W_2} > {W_1}$.

So, the correct answer is Option A,B,C.

Note: Generally the thermodynamic process proceeds in one single direction only that is their preferred direction and there exists the process that can happen in both directions and such are known as reversible process or equilibrium process.