1 mole of an ideal gas, initially at 400 K and 10 atm is first expanded at constant pressure till the volume is doubled.Then the gas is made to undergo an isochoric process, in which its temperature is found to decreases.In the last final step, gas was compressed reversibly and adiabatically to initial state.Determine the net work involved in this cyclic process (in terms of R).Given, C_v for gas =1.5 R, (4)^(-1//3)=0.63 If |W|=2Rxxz, report your answer as z.

1 mole of an ideal gas, initially at 400 K and 10 atm is first expande

1.	1 mole of an ideal gas, initially at 400 K and 10 atm is first expanded at constant pressure till the volume is doubled.Then the gas is made to undergo an isochoric process, in which its temperature is found to decreases.In the last final step, gas was compressed reversibly and adiabatically to initial state.Determine the net work involved in this cyclic process (in terms of R).Given, C_v for gas =1.5 R, (4)^(-1//3)=0.63 If \|W\|=2Rxxz, report your answer as z.
Answer» <P> Solution :The PROCESS can be described on a p-V diagram as `{:(At1:p=10"atm",T=400K,V=V_1),(AT2:p=10"atm",T=800K,V=V_2=2V_1),(AT3:p=?,T=T_3,V=V_3=V_2=2V_1):}` Therefore, `W_12=-pDeltaV=-nRT=-400 R` `W_23=0 " " [because DeltaV=0]` Between 3 and 1 ,`TV^(gamma-1)` =constant `T_3(2V_1)^(gamma-1)=400(V_1)^(gamma-1)` `implies T_3=400(1/2)^(2//3)=252 K` `implies W_31=DeltaE_31=nCV(T_1-T_3)=3/2R(400-252)=222 R` `implies W_(12-31)=W_(12)+W_23+W_31= -178 R`