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(B) The internal energy $U$ of $n$ moles of an ideal gas is given by the formula: $U = \frac{f}{2} n R T$,where $f$ is the number of degrees of freedo

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$5$

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(B) The internal energy $U$ of $n$ moles of an ideal gas is given by the formula: $U = \frac{f}{2} n R T$,where $f$ is the number of degrees of freedom,$n$ is the number of moles,$R$ is the universal gas constant,and $T$ is the absolute temperature in Kelvin.Given: $n = 3$,$T = 27^{\circ} C = 27 + 273 = 300 \ K$,and $U = 2250 R$.Substituting these values into the formula:$2250 R = \frac{f}{2} 	imes 3 	imes R 	imes 300$$2250 = \frac{f}{2} 	imes 900$$2250 = f 	imes 450$$f = \frac{2250}{450} = 5$.Therefore,the number of degrees of freedom of the gas is $5$.

If the internal energy of $3$ moles of a gas at a temperature of $27^{\circ} C$ is $2250 R$,then the number of degrees of freedom of the gas is (where $R$ is the universal gas constant).

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