question_answer

Starting with the same initial conditions, an ideal gas expands from volumes\[{{V}_{1}}\]to\[{{V}_{2}}\]three different ways, the work done by the gas is \[{{W}_{1}}\] if the process is purely isothermal, \[{{W}_{2}}\] if purely isobaric and W3 if purely adiabatic, then

A)  \[{{W}_{2}}>{{W}_{1}}>{{W}_{3}}\]  

B)  \[{{W}_{2}}>{{W}_{3}}>{{W}_{1}}\]

C)  \[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\]

D)  \[{{W}_{1}}>{{W}_{3}}>{{W}_{2}}\]

Correct Answer: A

Solution :

 The corresponding p-V graph (also called indicator diagram) in three different processes will be shown. Area under the graph gives the work done by the gas. \[{{(Area)}_{2}}>{{(Area)}_{1}}>{{(Area)}_{3}}\] \[\therefore \] \[{{W}_{2}}>{{W}_{1}}>{{W}_{3}}\]