First slide

Heat given

Question

The amount of heat energy required to raise the temperature of 1 g of helium at NTP, from T₁ K to T₂ K is

Moderate

A

$\frac{3}{8} N_{A} k_{B} (T_{2} - T_{1})$
B

$\frac{3}{2} N_{A} k_{B} (T_{2} - T_{1})$
C

$\frac{3}{4} N_{A} k_{B} (T_{2} - T_{1})$
D

$\frac{3}{4} N_{A} k_{B} (\frac{T_{2}}{T_{1}})$

Solution

We know that, $Q = \frac{f}{2} n R Δ T$
For helium, $f = 3 and n = \frac{1}{4}$
$∴$ Amount of heat required,
$\begin{aligned} Q = \frac{3}{2} \times \frac{1}{4} \times k_{B} N_{A} Δ T \\ = \frac{3}{8} N_{A} k_{B} (T_{2} - T_{1}) \end{aligned}$

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