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Question

(B) The internal energy $U$ of a gas molecule with $f$ degrees of freedom is given by $U = \frac{f}{2} k_B T$. Given: $f = 6$,$T = 47^{\circ} C = 47 +

Vedclass · Accepted Answer

$828 	imes 10^{-4}$

Vedclass · Answer

(B) The internal energy $U$ of a gas molecule with $f$ degrees of freedom is given by $U = \frac{f}{2} k_B T$. Given: $f = 6$,$T = 47^{\circ} C = 47 + 273 = 320 \ K$,and $k_B = 1.38 	imes 10^{-23} \ J \ K^{-1}$. Substituting the values: $U = \frac{6}{2} 	imes (1.38 	imes 10^{-23}) 	imes 320 = 3 	imes 1.38 	imes 320 	imes 10^{-23} \ J$. $U = 1324.8 	imes 10^{-23} \ J$. To convert energy from Joules to $eV$,divide by the charge of an electron $(1.6 	imes 10^{-19} \ C)$: $U_{eV} = \frac{1324.8 	imes 10^{-23}}{1.6 	imes 10^{-19}} \ eV = 828 	imes 10^{-4} \ eV$. Thus,the correct option is $B$.

If the degrees of freedom of a gas molecule is $6$,then the total internal energy of the gas molecule at a temperature of $47^{\circ} C$ (in $eV$) is (Boltzmann constant $= 1.38 \times 10^{-23} \ J \ K^{-1}$)

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