question_answer 35)

                  A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in fig. Find heat exchanged by the engine, with the surroundings for each section of the cycle. \[({{C}_{\upsilon }}\,=(3/2)R)\]                 AB : constant volume                 BC : constant pressure                 CD : adiabatic                 DA : constant pressure                

Answer:

                  (a) Refer part (d) of Q. No. 12.34 (b) \[Q=d{{U}_{BC}}+d{{W}_{BC}}\]                 Now \[d{{V}_{BC}}=\,{{C}_{\upsilon }}\,({{T}_{C}}-{{T}_{B}})=\,\frac{3}{2}\,R\,({{T}_{C}}\,-{{T}_{B}})\]                 \[=\frac{3}{2}\,(R{{T}_{C}}-\,R{{T}_{B}})\,=\frac{3}{2}\,\,({{P}_{B}}{{V}_{C}}-{{P}_{B}}{{V}_{B}})\]                 \[=\frac{3}{2}\,{{P}_{B}}\,({{V}_{C}}-{{V}_{B}})\]                 and \[d{{W}_{BC}}=PB\text{ }({{V}_{C}}-{{V}_{B}})\]                 \[\therefore \] \[Q=\frac{5}{2}\,{{P}_{B}}\,({{V}_{C}}-{{V}_{B}})\]                 (c) \[{{Q}_{CD}}=0\]  (as no heat is exchanged between system and its surrounding during adiabatic process)                 (d) Proceed as in (b)                 \[Q=\,\frac{5}{2}\,{{P}_{A}}\,({{V}_{A}}-{{V}_{D}})\]