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(C) The kinetic energy $(KE)$ of an ideal gas is given by the formula $KE = nRT$,where $n$ is the number of moles,$R$ is the universal gas constant,an

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$533$

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(C) The kinetic energy $(KE)$ of an ideal gas is given by the formula $KE = nRT$,where $n$ is the number of moles,$R$ is the universal gas constant,and $T$ is the temperature in Kelvin.For helium: $n_1 = 0.3 \ mol$,$T_1 = T$.$KE_{He} = 0.3 	imes R 	imes T$.For argon: $n_2 = 0.4 \ mol$,$T_2 = 400 \ K$.$KE_{Ar} = 0.4 	imes R 	imes 400$.According to the problem,$KE_{He} = KE_{Ar}$.$0.3 	imes R 	imes T = 0.4 	imes R 	imes 400$.Dividing both sides by $R$:$0.3 	imes T = 160$.$T = \frac{160}{0.3} = 533.33 \ K \approx 533 \ K$.

What is the temperature at which the kinetic energy of $0.3 \ mol$ of helium is equal to the kinetic energy of $0.4 \ mol$ of argon at $400 \ K$ (in $K$)?

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