Heat and Thermodynamics 6 Question 29
34. An insulated box containing a monoatomic gas of molar mass $M$ moving with a speed $v _0$ is suddenly stopped. Find the increment in gas temperature as a result of stopping the box.
(2003, 2M)
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Answer:
Correct Answer: 34. $\Delta T=\frac{M v_0^2}{3 R}$
Solution:
- Decrease in kinetic energy $=$ increase in internal energy of the gas
$$ \begin{aligned} & \therefore & \frac{1}{2} m v _0^{2}=n C _V \Delta T & =\left(\frac{m}{M}\right)\left(\frac{3}{2} R\right) \Delta T \\ & \therefore & \Delta T & =\frac{M v _0^{2}}{3 R} \end{aligned} $$
