The amount of heat energy required to raise the temperature of 1 g of helium at NTP, from $T_1 \mathrm{~K}$…

The amount of heat energy required to raise the temperature of 1 g of helium at NTP, from $T_1 \mathrm{~K}$ to $T_2 \mathrm{~K}$ is
  1. $\frac{3}{8} N_2 K_B\left(T_2-T_1\right)$
  2. $\frac{3}{2} N_2 K_B\left(T_2-T_1\right)$
  3. $\frac{3}{4} N_2 K_B\left(T_2-T_1\right)$
  4. $\frac{3}{4} N_2 K_B\left(\frac{T_2}{T_1}\right)$

Solution

We know that $Q=\frac{F}{2} n R \Delta T$
$\therefore$ Amount of heat required,
$\begin{aligned}
Q & =\frac{3}{2} \times \frac{1}{4} \times K_B N_B \Delta T \\
& =\frac{3}{8} N_B K_B\left(T_2-T_1\right)
\end{aligned}$ *

Asked in: NEET 2013 (All India)

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