Question

One mole of an ideal monoatomic gas is heated at a constant pressure from $0$ to $100$. Then the change in the internal energy of the gas is:

(Given, $R=8.32J{mol}^{-1}{K}^{-1}$)

• A. $0.83\times {10}^{3}J$
• B. $4.6\times {10}^{3}J$
• C. $2.08\times {10}^{3}J$
• D. $1.25\times {10}^{3}J$

Answer 1

Answer: (D)

$1.25\times {10}^{3}J$

Given : $T_i=0^{o}C=273K$ $T_f={100}^{o}C=373K$ $n=1$

For monoatomic gas $C_v=\frac{3R}{2}$

$\therefore$ Change in internal energy of the gas $\Delta U=n{C}_v\Delta T$

$\Delta U=\frac{3R}{2}n(T_f-T_i)=1\times \frac{3}{2}\times 8.314\times (373-273)$

$⟹$ $\Delta U=1.25\times {10}^3$ $J$