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Physics-

General

Easy

Question

The temperature of a gas is -68 $℃$ . At what temperature will the average kinetic energy of its molecules be twice that of at -68 $℃$ ?

$137 ℃$
127 $℃$
100 $℃$
105 $℃$

The correct answer is: $137 ℃$

Average kinetic theory of one molecule is
$E equals fraction numerator 3 over denominator 2 end fraction k T$
where $k$ is Boltzmann constant and $T$ the absolute temperature.
Given, $T subscript 1 end subscript equals negative 68 ℃ equals 273 minus 68 equals 205 blank K comma$
$E subscript 1 end subscript equals E comma blank E subscript 2 end subscript equals 2 E$
$therefore blank fraction numerator E subscript 1 end subscript over denominator E subscript 2 end subscript end fraction equals fraction numerator T subscript 1 end subscript over denominator T subscript 2 end subscript end fraction$
$rightwards double arrow blank T subscript 2 end subscript equals fraction numerator T subscript 1 end subscript E subscript 2 end subscript over denominator E subscript 1 end subscript end fraction$
$therefore blank T subscript 2 end subscript equals fraction numerator 205 cross times 2 E over denominator E end fraction equals 410 blank K$

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