What will be the average value of energy along one degree of...

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature

T ?

(

{k}_{B}

is Boltzmann constant)

Options

A $\dfrac{1}{2}{k}_{B}T$
B $\dfrac{2}{3}{k}_{B}T$
C $\dfrac{3}{2}{k}_{B}T$
D ${k}_{B}T$

Correct answer

A. $\dfrac{1}{2}{k}_{B}T$

Step-by-step solution

Energy associated with each degree of freedom per molecule $= \dfrac{1}{2}{k}_{B}T .$

Hence, the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $T =$ $\dfrac{1}{2}{k}_{B}T .$

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