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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 $f = 5$.Given: Pressure $P = 8 	imes 10^4\, N/m^2$,Mass $m = 1\, kg$,Density $ho = 4\, kg/m^3$.The volume $V$ is calculated as $V = \frac{m}{ho} = \frac{1}{4} = 0.25\, m^3$.Substituting the values into the energy formula:$U = \frac{5}{2} 	imes (8 	imes 10^4) 	imes (0.25)$$U = \frac{5}{2} 	imes 8 	imes 10^4 	imes \frac{1}{4}$$U = 5 	imes 10^4\, J$.

$1\, kg$ of a 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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