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Question

In a cylinder, 2.0moles of an ideal monatomic gas initially at 1.0×106Pa and 300K expands until its volume doubles. Compute the work done if the expansion is isothermal, adiabatic and isobaric.

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Solution

Let P1=1.0×106Pa=106N/m2; T1=300K; n=2moles.
Finalvolume=2(initialvolume)V2=2V1
W(isothermal)=2.303nRTlog(V2V1)
W=2.303×2×8.3×300log2
W=3452J
W(adiabatic)=nR(T1T2)γ1
For adiabatic process: T1V1γ1=T2V2γ1
T2=T1=(V2V1)γ1=300×(12)(53)1T2=189K
W=nR(T1T2)γ1=2×8.3×(300189)(53)1W=2764J
W(isobaric)=P(V2V1)P1V1=nRT1
V1=nRT1P1=2×8.3×300106V1=4.98×103m3
W=P(V2V1)=P(2V1V1)=PV1
W=106×4.98×103JW=4980J

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