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Question

${3 \over 2}RT$

${9 \over 2}RT$

${5 \over 2}RT$

3RT

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Step-by-Step Solution Step 1: Identify the type of gas and degrees of freedom A diatomic gas (such as O2 or N2) has 3 translational degrees of freedom and 2 rotational degrees of freedom if it is non-linear (for most diatomic molecules at normal temperatures, the third rotational mode may become active at higher temperatures). However, typically, we consider 3 translational + 3 rotational degrees of freedom, giving a total of 6 effective degrees of freedom at typical conditions. Step 2: Write down the formula for internal energy The internal energy $U$ of an ideal gas is given by the formula $U = \frac{f}{2} n R T$ where: $f$ = total degrees of freedom $n$ = number of moles $R$ = universal gas constant $T$ = absolute temperature Step 3: Substitute known values Given: $f = 6$ $n = 1$ mole So, $U = \frac{6}{2} \times 1 \times R T = 3 R T$ Step 4: State the final answer Hence, the total internal energy of the given diatomic gas is $3\,RT$.

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