Question

One mole of an ideal monoatomic gas is heated at a constant pressure from $0^{\circ} C$ to $100^{\circ} C$. Then the change in the internal energy of the gas is (Given $R=8.32 \,J\,mol ^{-1} \,K ^{-1}$ )

• A. $0.83 ? 10^3 \,J$
• B. $4.6 ? 10^3\, J$
• C. $2.08 ? 10^3 \,J$
• D. $1.25 ? 10^3\, J$

Answer 1

Answer: (D)

$1.25 ? 10^3\, J$

Answer 2

We know that $\Delta U=n C_{v} \Delta T$
where $\Delta T=\left(T_{2}-T_{1}\right)$
$T_{1}=0^{\circ} C =273\, K$
$T_{2} =100^{\circ} C =373\, K$
$n =1$ (monoatomic gas)
$R=8.32\, J \,,mol ^{-1} K ^{-1}=1 \times \frac{3}{2} R \times(373-273)$
$=1 \times \frac{3}{2} \times 8.32 \times 100=3 \times 8.32 \times 50$
$\Rightarrow 1248 \,kJ$
or $=1.25 \times 10^{3} \,J$