Question

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

• A. $\left(\frac{3}{8}\right){\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}({\mathrm{T}}_2-{\mathrm{T}}_1)$
• B. $\left(\frac{3}{2}\right){\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}({\mathrm{T}}_2-{\mathrm{T}}_1)$
• C. $\left(\frac{3}{4}\right){\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}({\mathrm{T}}_2-{\mathrm{T}}_1)$
• D. $\left(\frac{3}{8}\right){\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}\left(\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}\right)$

Answer 1

The correct option is A

$\left(\frac{3}{8}\right){\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}({\mathrm{T}}_2-{\mathrm{T}}_1)$

Given, that the mass of the helium sample= 1 gram

Molecular mass of helium = 4 gram

Number of moles of helium (n)=$\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molecular}\mathrm{mass}}=\frac{1}{4}\mathrm{mole}$

Change in temperature (ΔT)= (T₂ – T₁)

C_v = (3/2)R

C_v = Specific heat at constant volume

The amount of heat energy required (ΔQ) = nC_vΔT

The amount of heat energy required (ΔQ) = $\left[\frac{1}{4}\right]\left[\frac{3}{2}\right]\mathrm{R}({\mathrm{T}}_2-{\mathrm{T}}_1)$

The amount of heat energy required (ΔQ) = $\left[\frac{3}{8}\right]\mathrm{R}({\mathrm{T}}_2-{\mathrm{T}}_1)=\left[\frac{3}{8}\right]{\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)$

Here, R = N_Ak_B

where k_B is Boltzmann constant and N_A is Avogadro’s number

Hence, Option (A) is correct.