Internal energy of n_1 moles of hydrogen at t | vedclass

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Question

(B) The internal energy $U$ of an ideal gas is given by the formula $U = n \frac{f}{2} RT$,where $n$ is the number of moles,$f$ is the degree of freed

Vedclass · Accepted Answer

$6$:$5$

Vedclass · Answer

(B) The internal energy $U$ of an ideal gas is given by the formula $U = n \frac{f}{2} RT$,where $n$ is the number of moles,$f$ is the degree of freedom,$R$ is the universal gas constant,and $T$ is the absolute temperature.For $n_1$ moles of hydrogen $(H_2)$ at temperature $T$ with $f_1 = 5$:$U_1 = n_1 	imes \frac{5}{2} 	imes R 	imes T$For $n_2$ moles of helium $(He)$ at temperature $2T$ with $f_2 = 3$:$U_2 = n_2 	imes \frac{3}{2} 	imes R 	imes (2T)$Given that $U_1 = U_2$:$n_1 	imes \frac{5}{2} 	imes RT = n_2 	imes \frac{3}{2} 	imes R 	imes 2T$Canceling $\frac{1}{2}$,$R$,and $T$ from both sides:$5n_1 = 6n_2$Therefore,the ratio $\frac{n_1}{n_2} = \frac{6}{5}$.

Internal energy of $n_1$ moles of hydrogen at temperature $T$ is equal to the internal energy of $n_2$ moles of helium at temperature $2T$. Then the ratio $n_1:n_2$ is: [Degree of freedom of $He = 3$,Degree of freedom of $H_2 = 5$]

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