Question

If the internal energy of $n_{1}$ moles of Heat temperature $10\, T$ is equal to the internal energy of $n_{2}$ mole of hydrogen at temperature $6\, T$. The ratio of $n_{1} / n_{2}$ is

• A. 3/5
• B. 2
• C. 1
• D. 5/3

Answer 1

Answer: (C)

The internal energy of a gas is given by
$U=n C_{V} T$
Since, $U_{H e}=U_{H_{2}}$
So $n_{H e} C_{V} T_{H e}=n_{H_{2}} C_{V} T_{H_{2}}$
For $He$, the value of $C_V$
$C_{V}=\frac{5}{2} R$
For $H$, the valve of $C_{V}$
$C_{V}-\frac{3}{2} R$
$\therefore n_{H e} \times \frac{3}{2} R \times 10\, T$
$=n_{H} \times \frac{5}{2} \times 6\, T$
or $\frac{n_{H e}}{n_{H}}=1$
or $\frac{n_{1}}{n_{2}}=1$