An ideal gas is carried through a thermodynamic cycle consisting of two isobaric and two isothermal processes as shown in figure. Show that the net work done in the entire cycle is given by the equation. `W_(n et)=p_1(V_2-V_1) In(p_2)/(p_1)`

Answer

A

Explanation

Along the process CD apply,
`pV=` constant and find `V_C`
Similarly along path AB, again apply,
`pV=` constant and find `V_B`.
Now, `W_(n et)=W_(AB)+W_(BC)+W_(CD)+W_(DA)`
`=nRT_A In ((V_B)/(V_A))+p_B(V_C-V_B)`
`+nRT_C In ((V_D)/(V_C))+p_D(V_A-V_D)`
Further, `nRT_A=p_AV_A`
and `nRT_C=p_CV_C`