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(B) The internal energy $U$ of $n$ moles of an ideal gas is given by $U = \frac{f}{2} nRT$,where $f$ is the degrees of freedom.For a diatomic gas,the

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$5 	imes 10^4\, J$

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(B) The internal energy $U$ of $n$ moles of an ideal gas is given by $U = \frac{f}{2} nRT$,where $f$ is the degrees of freedom.For a diatomic gas,the degrees of freedom $f = 5$.Since we are given the mass $m = 1\, kg$,we use the relation for energy per unit mass: $E = \frac{f}{2} rT$,where $r$ is the specific gas constant $(r = R/M)$.From the ideal gas equation $PV = nRT$,we have $P = ho rT$,which implies $rT = \frac{P}{ho}$.Substituting the given values: $P = 8 	imes 10^4\, N/m^2$ and $ho = 4\, kg/m^3$.$E = \frac{5}{2} 	imes \frac{P}{ho} = \frac{5}{2} 	imes \frac{8 	imes 10^4}{4}$.$E = 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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