One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: J/kg.K$, the magnitude of work transfer is ________ $kJ$ (round off to $2$ decimal places).

T1=273+127=400K

V2=2V1→V2/V1=2

and P=C [P1=P2=P]

.'.PV=mRT   (P= constant)

V∝T

V2/V1=T2/T1

V2/V1=2 and T2/T1=2

T2=2T1

T2=2×400=800K

work=P(V2-V1)

W=PV2-PV1

W=mRT2-mRT1 [P1=P2=P]

W=mR(T2-T1)

W=1×0.287×(800-400)

w=114.8KJ Ans

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