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Physics

Heat

Easy

Question

During an experiment an ideal gas is found to obey an additional law VP² = constant. The gas is initially at temperature T and volume V. What wiII be the temperature of the gas when it expands to a volume 2V?

$(\sqrt{2}) T$
2T
$\frac{3 T}{2}$
$(\sqrt{3}) T$

The correct answer is: $left parenthesis square root of 2 right parenthesis T$

According to the given problem VP²= constant. So the gas PV=nRT in the light of above (eliminating P) yields. $open parentheses fraction numerator K over denominator square root of V end fraction close parentheses V equals n R T$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell text i.e. end text end cell row cell square root of V equals fraction numerator n R over denominator K end fraction T end cell end table square root of V subscript 1 over V subscript 2 end root equals open parentheses T subscript 1 over T subscript 2 close parentheses comma text i.e, end text square root of fraction numerator V over denominator 2 V end fraction end root equals T over T to the power of straight prime comma text or end text T to the power of ∗ equals left parenthesis square root of 2 right parenthesis T$

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