Question

The amount of heat energy required to raise the temperature of $1\text{gm}$ of Helium at $\text{NTP}$, from $T_1\text{K}\text{to}{T}_2\text{K}$ is-

• A. $\frac{3}{4}N{k}_B\left(\frac{T_2}{T_1}\right)$
• B. $\frac{3}{8}N{k}_B(T_2-T_1)$
• C. $\frac{3}{2}N{k}_B(T_2-T_1)$
• D. $\frac{3}{4}N{k}_B(T_2-T_1)$

Answer 1

The correct option is B $\frac{3}{8}N{k}_B(T_2-T_1)$

Number of moles in $1\text{gm of He}=\frac{1}{4}$

Amount of heat energy required to raise its temperature from $T_1\text{K}\text{to}{T}_2\text{K}$ is, (assuming the process takes place at constant volume)

$Q=n{C}_v\Delta T$

$\text{For a mono atomic gas,}{C}_v=\frac{3}{2}R$

$\therefore Q=\left(\frac{1}{4}\right)\left(\frac{3}{2}R\right)(T_2-T_1)$

$=\frac{3}{8}N{k}_B(T_2-T_1)$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.