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(C) The average kinetic energy $(E)$ of gas molecules is directly proportional to the absolute temperature $(T)$ in Kelvin: $E \propto T$.Given the in

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$313$

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(C) The average kinetic energy $(E)$ of gas molecules is directly proportional to the absolute temperature $(T)$ in Kelvin: $E \propto T$.Given the initial temperature $T_1 = 20^{\circ}C = 20 + 273 = 293 \, K$.We want the final kinetic energy $E_2$ to be twice the initial kinetic energy $E_1$,so $E_2 = 2E_1$.Using the ratio: $\frac{E_1}{E_2} = \frac{T_1}{T_2}$.Substituting the values: $\frac{E_1}{2E_1} = \frac{293}{T_2}$.$T_2 = 2 	imes 293 = 586 \, K$.Converting back to Celsius: $T_2(^{\circ}C) = 586 - 273 = 313^{\circ}C$.

At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at $20^{\circ}C$ (in $^{\circ}C$)?

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