The variation of internal energy U and density d of one mole of an ideal monatomic gas is shown inn cyclic process ABCA. The curve from A to B is a rectangular hyperbola. Select correct alternatives.

Options

A. The work done by gas in process `AB` is `2U_(0)`
B. The work done by gas in process BC is `-(3U_(0))/(2)ln2`
C. The molar heat capacity of gas for process CA is `(3R)/(2)`
D. The molar heat capacity of gas for process AB is `(3R)/(2)`

Answer

A, C

Explanation

`PM=dRT`
in `ABdprop(1)/(T)` therefore it is an isoberic process.
`W_(AR)=nRDeltaT=R(4T_(0)-T_(0))`
`U_(0)=(3)/(2)RT_(0)`
`W_(AB)=2U_(0)`
In process BC (isothermal)
`W_(BC)=-nR(4T_(0))ln((4d_(0))/(d_(0)))=-8RT_(0)ln2`
`=-(16)/(3)U_(0)ln2`
Process CA is isochoric while AB is isobaric