Question

Two moles of an ideal monoatomic gas are expanded according to the equation PT = constant from 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

• 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 $U=1.5nRT$
also from ideal gas equation $PV=nRT$
here $n=1$----(monoatomic)
so we get $PV=RT$
we get $\Delta U=1.5P_0{V}_0$
or $\Delta U=\frac{3P_0{V}_0}{2}$