A 1 , kg diatomic gas is at a pressure of 8 t | vedclass

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(C) For a diatomic gas,the degrees of freedom $f = 5$.The total internal energy (thermal energy) is given by $U = \frac{f}{2} \mu RT$.We know that $\m

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$5 	imes 10^4 \, J$

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(C) For a diatomic gas,the degrees of freedom $f = 5$.The total internal energy (thermal energy) is given by $U = \frac{f}{2} \mu RT$.We know that $\mu = \frac{M}{M_0}$,where $M$ is the total mass and $M_0$ is the molar mass.From the ideal gas equation,$PV = \mu RT$,so $\mu RT = PV$.Also,density $ho = \frac{M}{V}$,which implies $V = \frac{M}{ho}$.Substituting these into the energy equation:$U = \frac{f}{2} PV = \frac{f}{2} P \left( \frac{M}{ho} ight)$.Given $f = 5$,$P = 8 	imes 10^4 \, N/m^2$,$M = 1 \, kg$,and $ho = 4 \, kg/m^3$:$U = \frac{5}{2} 	imes (8 	imes 10^4) 	imes \left( \frac{1}{4} ight)$.$U = \frac{5}{2} 	imes 2 	imes 10^4 = 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 will be the energy associated with the thermal motion of the gas?

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