Rankers Physics
Topic: Thermal Physics
Subtopic: Kinetic Theory of Gases

The amount of heat energy required to raise the temperature of $1 \text{ g}$ of Helium at NTP, from $T_1 \text{ K}$ to $T_2 \text{ K}$ is: (2013)
$\frac{3}{4} N_A k_B \left(\frac{T_2}{T_1}\right)$
$\frac{3}{8} N_A k_B (T_2 - T_1)$
$\frac{3}{2} N_A k_B (T_2 - T_1)$
$\frac{3}{4} N_A k_B (T_2 - T_1)$

Solution:

Helium is a monoatomic gas ($C_v = \frac{3}{2}R$). The number of moles in $1 \text{ g}$ is $n = \frac{1}{4}$. The heat required is $Q = n C_v \Delta T = \frac{1}{4} \left(\frac{3}{2}R\right)(T_2 - T_1) = \frac{3}{8} N_A k_B (T_2 - T_1)$.

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