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(D) The internal energy $U$ of an ideal gas is given by $U = \frac{f}{2} PV$,where $f$ is the degrees of freedom,$P$ is the pressure,and $V$ is the vo

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$5 	imes 10^4 \, J$

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(D) The internal energy $U$ of an ideal gas is given by $U = \frac{f}{2} PV$,where $f$ is the degrees of freedom,$P$ is the pressure,and $V$ is the volume.For a diatomic gas,the degrees of freedom $f = 5$.The volume $V$ is given by $V = \frac{	ext{mass}}{	ext{density}} = \frac{1 \, kg}{4 \, kg/m^3} = 0.25 \, m^3$.Substituting the values: $U = \frac{5}{2} 	imes (8 	imes 10^4 \, N/m^2) 	imes (0.25 \, m^3)$.$U = 2.5 	imes 8 	imes 10^4 	imes 0.25 = 20 	imes 10^4 	imes 0.25 = 5 	imes 10^4 \, J$.

$A$ $1 \, kg$ diatomic gas is at a pressure of $8 \times 10^4 \, N/m^2$. The density of the gas is $4 \, kg/m^3$. What is the energy of the gas due to its thermal motion?

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