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Question

Two moles of an ideal monoatomic gas at 27C occupies a volume of V. If the gas is expanded adiabatically to the volume 23/2V, then the work done by the gas will be (γ=53,R=8.31 J/mol K)
  1. 3739.5 J
  2. 2627.23 J
  3. 2500 J
  4. 2500 J


Solution

The correct option is A 3739.5 J
Given, gas is monoatomic γ=53
Initial Temperature (Ti)=300 K
Initial volume (Vi)=V
Final volume (Vf)=23/2V
Work done by the gas (W)=nR(TiTf)γ1
=nRTiγ1[1TfTi]
As, TiVγ1i=TfVγ1f
W=nRTiγ1[1(ViVf)γ1]
=2×8.31×300(531)⎢ ⎢1(123/2)23⎥ ⎥
=3739.5 J

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