The amount of heat energy required to raise the temperature of $1 g$ of helium in a container of volume $10 L$ , from $T_{1} K$ to $T_{2} K$ is ( $N_{a} =$ Avogadros number, $k_{B} =$ Boltzmann constant)

\frac{3}{2} N_{a} k_{B} (T_{2} - T_{1})

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\frac{3}{7} N_{a} k_{B} (T_{2} - T_{1})

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\frac{3}{4} N_{a} k_{B} (T_{2} - T_{1})

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

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Solution

The correct option is D $\frac{3}{8} N_{a} k_{B} (T_{2} - T_{1})$
The process is being completed at a constant volume because the volume of the container is fixed.
so the heat energy required will be $Q = n C_{v} Δ T$
Where $C_{v}$ is specific heat at constant volume and $n$ is number of moles given by $n = \frac{1 g m}{4 g m / m o l e} = \frac{1}{4} m o l e$
and the specific heat is given as $C_{v} = \frac{f N_{a} k_{B}}{2}$
The degree of freedom, $f$ has value $3$ for a mono-atomic gas.
$N_{a}$ is Avogadro Number and $k_{B}$ is Boltzman's constant
putting all above values in the expression for $Q$ we get $Q = \frac{3}{8} N_{a} k_{B} Δ T = \frac{3}{8} N_{a} k_{B} (T_{2} - T_{1})$
Option D is correct.

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The amount of heat energy required to raise the temperature of 1 g of helium in a container of volume 10L, from T1 K to T2 K is (Na= Avogadros number, kB= Boltzmann constant)

The amount of heat energy required to raise the temperature of $1 g$ of helium in a container of volume $10 L$ , from $T_{1} K$ to $T_{2} K$ is ( $N_{a} =$ Avogadros number, $k_{B} =$ Boltzmann constant)