Molecules of an ideal gas are known to have three translational...

Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of \gamma = \left(\dfrac{{C}_{p}}{{C}_{v}}\right) are given, respectively, by

Options

A $U = \dfrac{5}{2}RT$ and $\gamma = \dfrac{6}{5}$
B $U = 5RT$ and $\gamma = \dfrac{7}{5}$
C $U = \dfrac{5}{2}RT$ and $\gamma = \dfrac{7}{5}$
D $U = 5RT$ and $\gamma = \dfrac{6}{5}$

Correct answer

C. $U = \dfrac{5}{2}RT$ and $\gamma = \dfrac{7}{5}$

Step-by-step solution

$f = 5$

$\gamma = 1 + \dfrac{2}{f} = 1 + \dfrac{2}{5} = \dfrac{7}{5}$

$\dfrac{{C}_{p}}{{C}_{v}} = \dfrac{7}{5}$

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