Question

2 moles of an ideal monoatomic gas is expanded according to relation $PT$ = constant from its initial state $\left(P_0{V}_0\right)$ to the final state, due to which its pressure becomes half of the initial pressure. The change in internal energy is

• A. $\frac{3}{4}{P}_0{V}_0$
• B. $\frac{3}{2}{P}_0{V}_0$
• C. $\frac{9}{2}{P}_0{V}_0$
• D. $\frac{5}{2}{P}_0{V}_0$

Answer 1

The correct option is B $\frac{3}{2}{P}_0{V}_0$

for mono - atomic gas $U=\frac{3}{2}nRT$
also from ideal gas equation $PV=nRT$
where P = pressure,
$V$ = volume
$n$ = number of mole
$R$ = universal gas constant
$T$ = Temperature
here $n=2$ (mono - atomic)
So we get $P_o{V}_o=2R{T}_0$
where $T_o$ is the initial temperature and $2T_o$ is the final temperature.
we know
$\Delta U=n{C}_V\Delta T$
or $\Delta U=n{C}_V{T}_o$
here, $\Delta U=$ change in internal energy
$n$ = number of moles
$C_V$ = heat capacity (constant volume)
$\Delta T$ = change in Temperature
or $\Delta U=\frac{3}{2}{P}_0{V}_0$