Question

An insulated box containing monatomic ideal gas of molar mass M is moving with a uniform speed v. The box suddenly stops and consequently the gas acquires a new temperature. Calculate the change in the temperature of the gas. Neglect heat absorbed by the box.

• A. $\Delta T=2\frac{M{v}^2}{3R}$.
• B. $\Delta T=\frac{M{v}^2}{3R}$.
• C. $\Delta T=3\frac{M{v}^2}{3R}$.
• D. $\Delta T=4\frac{M{v}^2}{3R}$.

Answer 1

The correct option is B $\Delta T=\frac{M{v}^2}{3R}$.

An insulated Box containing monoatomic ......... neglect heat absorbed by box

molar mass$=M$

speed $=v$

Initial energy $=KE=\frac{1}{2}M{V}^2$

Final energy = Temperature energy (or $PE$)

$=\frac{3}{2}RT$

For ideal conditions, $\frac{1}{2},m{v}^2=\frac{3}{2}RT$

$\Delta T=\frac{m{v}^2}{3R}$