Two moles of an ideal monoatomic gas are expanded according to the equation pT=constant form its initial state `(p_0, V_0)` to the final state due to which its pressure becomes half of the initial pressure. The change in internal energy is

Options

A. `(3)/(4)P_(0)V_(0)`
B. `(3)/(2)P_(0)V_(0)`
C. `(9)/(2)P_(0)V_(0)`
D. `(5)/(2)P_(0)V_(0)`

Explanation

`PT=`constant
`P_(0)T_(i)=(P_(0))/(2)T_(i)`
`rArr T_(f)=2T_(i)`
Also, `P_(0)V_(0)=2R.T_(i)`
`T_(i)=(P_(0)V_(0))/(2R)`….(`1`)
`P_(f)V_(f)=nR.T_(f)`
`rArr (P_(0))/(2)V_(f)=[2][R][2T_(f)]`…..(`2`)
`rArr T_(f)=(P_(0)V_(0))/(R )`
`:. DeltaU=(3)/(2)nRDeltaT=(3)/(2)P_(0)V_(0)`