At what temperature K will the kinetic energy | vedclass

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Question

(B) The kinetic energy $(KE)$ of an ideal gas is given by the formula $KE = \frac{3}{2} nRT$. Given that the kinetic energy of $He$ is equal to the ki

Vedclass · Accepted Answer

$500$

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(B) The kinetic energy $(KE)$ of an ideal gas is given by the formula $KE = \frac{3}{2} nRT$. Given that the kinetic energy of $He$ is equal to the kinetic energy of $Ar$: $KE_{He} = KE_{Ar}$ $\frac{3}{2} n_{He} R T_{He} = \frac{3}{2} n_{Ar} R T_{Ar}$ $n_{He} 	imes T_{He} = n_{Ar} 	imes T_{Ar}$ Substituting the given values: $0.3 	imes T_{He} = 0.4 	imes 400$ $0.3 	imes T_{He} = 160$ $T_{He} = \frac{160}{0.3} = 533.33 \ K$. Since the closest option provided is $533.33 \ K$ is not present,let us re-evaluate the question context. If the question implies average kinetic energy per mole,then $KE = \frac{3}{2} RT$. However,for total kinetic energy,the calculation holds. Given the options,$533.33 \ K$ is the correct mathematical result.

At what temperature $K$ will the kinetic energy of $0.3 \ mol$ of $He$ be equal to the kinetic energy of $0.4 \ mol$ of $Ar$ at $400 \ K$?

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