Q. Air is filled in a motor tube at $27℃$ and at a pressure of 8 atmosphere. The tube suddenly bursts, then temperature of air is [Given $\gamma$ of air = 1.5]
A) $27.5{^\circ}\ C$
B) $75{^\circ}\ K$
C) $150{^\circ}\ K$
D) $150{^\circ}\ C$
Explanation
(c) $\frac{T_{2}}{T_{1}} = \left( \frac{P_{2}}{P_{1}} \right)^{\frac{\gamma - 1}{\gamma}\ } \Rightarrow \frac{T_{2}}{T_{1}} = \left( \frac{1}{8} \right)^{\frac{1.5 - 1}{1.5}} = \left( \frac{1}{8} \right)^{\frac{1}{3}} = \frac{1}{2}$
$\Rightarrow T_{2} = \frac{T_{1}}{2} = \frac{300}{2} = 150K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.