In the following cyclic process abca, find the net heat given to the system. Take number of moles of ideas gas `n`.

Explanation

(a) When problem is in the form of diagram, first try to identify the process (if possible) and then proceed.
ab: Volume is constant i.e., `DeltaW_(ab)=0`
bc, Temperature is constant i.e, isothermal process
`DeltaW_(bc)=nR.2T_01n((2V_0)/(V_0))=2nRT_01n2`
ca: `V-T` diagram is an inclined line passing through origin i.e, isobaric process
`DeltaW_(ca)=PDeltaV=nRDeltaT=nR(T_0-2T_0)`
`=-nRT_0`
`DeltaW_(cyclic)=DeltaW_(ab)+DeltaW_(bc)+DeltaW_(ca)`
`=0+21n2nRT_0-nRT_0`
`=(21n2-1)nRT_0=DeltaQ_(cyclic)`
(b) ab: `T-V` diagram is an inclined line passing through origin i.e., isobaric process
`DeltaW_(ab)=PDeltaV=nRT=nR(T_b-T_a)`
`=2xx2(500-300)=800cal`
ca: Volume is contant, `DeltaW_(ca)=0`
In cyclic process, `DeltaQ=DeltaW`
`DeltaQ=DeltaW_(ab)+DeltaW_(bc)+DeltaW_(ca)`
`-1000=800+DeltaW_(bc)+0`
`DeltaW_(bc)=-1800cal`
(c) ab: Internal energy is constant i.e, isothermal process
`DeltaW_(ab)o=nRT_(b)1n((2V_0)/(V_0))=nRT_01n2`
bc: isochoric process, `DeltaW_(bc)=0`
cd: Isothermal process,
`DeltaW_(ca)=nRT_c1n((V)/(2V_0))=-nRT_c1n2`
da: Isochoric process, `DeltaW_(da)=0`
`W_(cyclist)=DeltaW_(ab)+DeltaW_(bc)+DeltaW_(cd)+DeltaW_(da)`
`=nRT_b1n2+0-nRT_c1n2+0`
`=nR(T_b-T_c)1n2`
`=2xx2(400-300)xx0.693`
`=277.2cal`
In cyclic process, `DeltaQ_(cyclist)=DeltaW_(cyclic)=277.2cal`