Question

Figure, shows the variation of potential energy `(U)` of 2 mol of Argon gas with its density in a cyclic process `ABCA`. The gas was initiallly in the state `A` whose pressure and temperature are `P_(A)=2 atm, T_(A)=300K`, respectively. It is also stated the path `AB` is a rectangular hyperbola and the internal energy of the gas at state `C` is `3000r`. Based on the above information answer the following question `:`

The heat supplied to the gas in the process `AB` is
A. `700R`
B. `3500R`
C. `4400R`
D. `1600R`

Answer 1

Correct Answer - B
Given `U_(C)=3000R=Nc_(v)T_(C)`
`implies 3000 r = 2 XX (3)/( 2) R xx T_(C)`
`implies T_(C)=1000K`
Also `U_(B)=U_(C)`
and `U_(A)= 2 xx(3)/(2) Rxx 300=900 R`
`W_(AB)=PDeltaV=n RDeltaT`
`=2 xx R(1000-300)`
`=1400R`
`U_(AB)=U_(B)-U_(A)=3000R-900R`
`=2100R`
`:. DeltaQ=DeltaW+DeltaU`
`=1400R+2100R=3500R`