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The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from $T_1$ K to $T_2$ K is:
A
$\frac{3}{4}N_ak_B\left(\frac{T_2}{T_1}\right)$
B
$\frac{3}{8}N_ak_B(T_2 - T_1)$
C
$\frac{3}{2}N_ak_B(T_2 - T_1)$
D
$\frac{3}{4}N_ak_B(T_2 - T_1)$
Detailed Solution
Number of moles in 1 g He $= \frac{1}{4}$
Heat required $= nC_v\Delta T = \frac{1}{4}\left(\frac{3}{2}R\right)(T_2 - T_1)$
$= \frac{3}{8}N_ak_B(T_2 - T_1)$
Heat required $= nC_v\Delta T = \frac{1}{4}\left(\frac{3}{2}R\right)(T_2 - T_1)$
$= \frac{3}{8}N_ak_B(T_2 - T_1)$