An ideal gas expands isothermally from a volume V_(1) " to " V_(2) and then compressef to original volume V_(1) adiabatically. Initial pressure is P_(1) and final pressure is P_(3) . The total work done is W. Then what is its value and its conditions.

An ideal gas expands isothermally from a volume V_(1) " to " V_(2) and

1.	An ideal gas expands isothermally from a volume V_(1) " to " V_(2) and then compressef to original volume V_(1) adiabatically. Initial pressure is P_(1) and final pressure is P_(3) . The total work done is W. Then what is its value and its conditions.
Answer» SOLUTION :Slope of adiabatic process at a given state (P,V,T) is more than the slope of isothermal process. The corresponding `P-V` GRAPH for the two processes is as shown in figure. In the graph, A,B is isothermal and BC is adiabatic. `W_(AB)`= POSITIVE (as volume is increasing) plus, `abs(W_(BC)) gt abs(W_(AB))`, as area under P-V graph gives the WORK done. Hence, `W_(AB)+W_(BC) = W lt 0` From the graph itself, it is CLEAR that `P_(3) gt P_(1)`