Q. Compressed by doing work on it 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
Explanation
(c) $\frac{T_{2}}{T_{1}} = \left( \frac{V_{1}}{V_{2}} \right)^{\gamma - 1} = 2 \Rightarrow \left( \frac{V_{2}}{V_{1}} \right)^{\gamma - 1} = \frac{1}{2} \Rightarrow \frac{V_{2}}{V_{1}} = \left( \frac{1}{2} \right)^{\frac{1}{\gamma - 1}} < \frac{1}{2}$
$\Rightarrow V_{2} < \frac{V_{1}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.