An ideal gas is in thermodynamic equilibrium. | vedclass

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(C) The internal energy of one mole of an ideal gas is given by $U_n = \frac{n}{2} RT$. Since $T$ is constant,$U_n$ is directly proportional to $n$. T

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$v_5 > v_7$ and $U_5 < U_7$

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(C) The internal energy of one mole of an ideal gas is given by $U_n = \frac{n}{2} RT$. Since $T$ is constant,$U_n$ is directly proportional to $n$. Therefore,if $n_1 The speed of sound in an ideal gas is given by $v_n = \sqrt{\frac{\gamma RT}{M}}$,where $\gamma = 1 + \frac{2}{n}$.Substituting $\gamma$,we get $v_n = \sqrt{\left(1 + \frac{2}{n}\right) \frac{RT}{M}}$.As $n$ increases,the term $(1 + \frac{2}{n})$ decreases,which means $v_n$ decreases as $n$ increases.Comparing options:For option $C$: $n=5$ and $n=7$. Since $5  v_7$. This matches the condition.

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure,which of the following is the correct option?

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