At what temperature in ^circ C will the kinet | vedclass

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Question

(C) The average kinetic energy of gas molecules is directly proportional to the absolute temperature: $E \propto T$.Given,$T_1 = 27^\circ C = 27 + 273

Vedclass · Accepted Answer

$327$

Vedclass · Answer

(C) The average kinetic energy of gas molecules is directly proportional to the absolute temperature: $E \propto T$.Given,$T_1 = 27^\circ C = 27 + 273 = 300 \ K$.Let the kinetic energy at $T_1$ be $E_1 = E$.We want the kinetic energy at $T_2$ to be $E_2 = 2E$.Using the relation $\frac{E_1}{E_2} = \frac{T_1}{T_2}$,we get:$\frac{E}{2E} = \frac{300}{T_2}$$\frac{1}{2} = \frac{300}{T_2}$$T_2 = 600 \ K$.Converting back to Celsius: $T_2(^\circ C) = 600 - 273 = 327^\circ C$.

At what temperature in $^\circ C$ will the kinetic energy of gas molecules be double the kinetic energy at $27^\circ C$?

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