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(D) For a diatomic gas,the internal energy $U$ is given by $U = \frac{f}{2} PV$,where $f$ is the degrees of freedom.For a diatomic gas,$f = 5$.Thus,$U

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$5 	imes 10^4 \ J$

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(D) For a diatomic gas,the internal energy $U$ is given by $U = \frac{f}{2} PV$,where $f$ is the degrees of freedom.For a diatomic gas,$f = 5$.Thus,$U = \frac{5}{2} PV$.Given:Pressure $P = 8 	imes 10^4 \ N/m^2$.Mass $m = 1 \ kg$.Density $ho = 4 \ kg/m^3$.Volume $V = \frac{m}{ho} = \frac{1 \ kg}{4 \ kg/m^3} = 0.25 \ m^3$.Substituting the values into the formula:$U = \frac{5}{2} 	imes (8 	imes 10^4 \ N/m^2) 	imes (0.25 \ m^3)$.$U = 2.5 	imes 8 	imes 10^4 	imes 0.25$.$U = 20 	imes 10^4 	imes 0.25 = 5 	imes 10^4 \ J$.

One 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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