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. `(3p_0V_0)/(4)`
B. `(3p_0V_0)/(2)`
C. `(9p_0V_0)/(2)`
D. `(5p_0V_0)/(2)`

Answer

B

Explanation

Pressure becomes half. So, temperature is doubled.
(as `Tprop1/p`)
`DeltaU=nC_VDeltaT`
`T_i=(p_0V_0)/(nR)`
`T_f=(2p_0V_0)/(nR)`
`:.` `Delta=T_f-T_i=(p_0V_0)/(nR)`
`:.` `DeltaU=n(3/2R)((p_0V_0)/(nR))=(3p_0V_0)/(2)`