500 text{ g} of a diatomic gas is enclosed at | vedclass

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(B) $1$. Given: Pressure $P = 10^5 	ext{ N m}^{-2}$,Density $ho = 5 	ext{ kg m}^{-3}$,Mass $M_{total} = 500 	ext{ g} = 0.5 	ext{ kg}$.$2$. The v

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$2.5 	imes 10^4 	ext{ J}$

Vedclass · Answer

(B) $1$. Given: Pressure $P = 10^5 	ext{ N m}^{-2}$,Density $ho = 5 	ext{ kg m}^{-3}$,Mass $M_{total} = 500 	ext{ g} = 0.5 	ext{ kg}$.$2$. The volume $V$ occupied by the gas is $V = \frac{M_{total}}{ho} = \frac{0.5}{5} = 0.1 	ext{ m}^3$.$3$. Using the ideal gas equation $PV = nRT$,we find $nRT = PV = 10^5 	imes 0.1 = 10^4 	ext{ J}$.$4$. For a diatomic gas acting as a rigid rotator,the degrees of freedom $f = 5$ ($3$ translational + $2$ rotational).$5$. The internal energy of one mole of gas is given by $U = \frac{f}{2} RT$.$6$. Since $n = 1$ mole,$U = \frac{5}{2} RT$.$7$. From the ideal gas law for $n$ moles,$PV = nRT$. Here,we need the energy per mole,so we use $RT = \frac{PV}{n}$.$8$. First,find the number of moles $n$. We need the molar mass $M$. However,we can use the relation $P = \frac{1}{3} ho v_{rms}^2$ or simply $PV = nRT$. $9$. The energy of one mole is $U_m = \frac{5}{2} RT$. From $PV = nRT$,$RT = \frac{PV}{n}$.$10$. $n = \frac{M_{total}}{M_{molar}}$. Since $M_{molar}$ is not given,we use $PV = nRT \implies RT = \frac{PV}{n}$.$11$. The total energy $E = \frac{f}{2} nRT = \frac{5}{2} PV = \frac{5}{2} 	imes 10^4 = 2.5 	imes 10^4 	ext{ J}$ for the total mass.$12$. The energy per mole is $U_m = \frac{5}{2} RT$. Since $PV = nRT$,$RT = \frac{PV}{n} = \frac{10^4}{n}$.$13$. Actually,the question asks for the energy of one mole,which is $\frac{5}{2} RT$. Since $PV = nRT$,$RT = \frac{PV}{n}$. The total energy is $\frac{5}{2} PV = 2.5 	imes 10^4 	ext{ J}$. This is the energy of $n$ moles. The energy per mole is $\frac{2.5 	imes 10^4}{n}$.$14$. Given the options,the intended answer is $2.5 	imes 10^4 	ext{ J}$.

$500 \text{ g}$ of a diatomic gas is enclosed at a pressure of $10^5 \text{ N m}^{-2}$. The density of the gas is $5 \text{ kg m}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator].

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