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11.Thermodynamics
medium
A gas is compressed adiabatically till its temperature is doubled. The ratio of its final volume to initial volume will be
A
$1/2$
B
More than $1 / 2$
C
Less than $1 / 2$
D
Between $1$ and $2$
Solution
(c) $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma – 1}} = 2 \Rightarrow {\left( {\frac{{{V_2}}}{{{V_1}}}} \right)^{\gamma – 1}} = \frac{1}{2} \Rightarrow \frac{{{V_2}}}{{{V_1}}} = {\left( {\frac{1}{2}} \right)^{\frac{1}{{\gamma – 1}}}} < \frac{1}{2}$
==> ${V_2} < \frac{{{V_1}}}{2}$
Standard 11
Physics
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