One mole of monoatomic gas is taken through cyclic process shown below. TA $$=$$ $$300$$ K. Process AB is defined as PT $$=$$ constant.

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(a) Process AB :          $$PT=$$ constant ⇒ $$nRT2V=$$ constant    $$W=$$∫AB $$PdV=$$∫AB Constant TdV⇒ $$dVdT=2nRT$$ Constant       $$W=$$∫$$300100$$ Constant T⋅$$2nRT$$ Constant dt⇒ $$PAPB=TBTA$$⇒ $$13=TBTA$$⇒ $$TB=3003=100$$⇒ $$W=2nR(100$$−$$300)$$⇒ $$WAB=$$−$$400nR(b)$$ Process CA : Isochoric, so PT is constant :             $$TATC=PAPC$$        $$TATC=PAPB$$⇒ $$TATC=13$$⇒ $$TC=3TA$$           $$TC=900R$$⇒ Δ$$U=nCV$$ΔT                $$=(1)32R$$×TA−TC                $$=32R$$×(300$$−$$900)                $$=32R$$×−$$600=$$−$$900R$$⇒ |ΔU|$$=(900R)(c)$$ Process BC:  Isobaric          $$Q=nCP$$ΔT⇒$$Q=(1)52R$$×TC−TB    $$Q=52R$$×(900$$−$$100)⇒$$Q=52R$$×$$800$$⇒$$Q=2000R$$

One mole of monoatomic gas is taken through cyclic process shown below. TA = 300 K. Process AB is defined as PT = constant.

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