question_answer

An ideal gas expands isothermally from a volume \[{{V}_{1}}\] to \[{{V}_{2}}\] and then compressed to original volume \[{{V}_{1}}\]adiabatically. Initial pressure is \[{{P}_{1}}\] and final pressure is \[{{P}_{3}}\]. The total work done is W. Then [IIT-JEE (Screening) 2004]

A)            \[{{P}_{3}}>{{P}_{1}},\,\,W>0\]                                       

B)            \[{{P}_{3}}<{{P}_{1}},\,\,W<0\]

C)            \[{{P}_{3}}>{{P}_{1}},\,\,W<0\]                                       

D)            \[{{P}_{3}}={{P}_{1}},\,\,W=0\]

Correct Answer: C

Solution :

                   From graph it is clear that \[{{P}_{3}}>{{P}_{1}}\]. Since area under adiabatic process (BCED) is greater than that of isothermal process (ABDE). Therefore net work done \[W={{W}_{i}}+(-{{W}_{A}})\] \[\because \ {{W}_{A}}>{{W}_{i}}\]  Þ  \[W<0\]