QJEEM11Phf84a: JEE Main 2011 Physics - Class 11 JEEM11Phf84a Solution: A thermally insulated vessel contains an ideal gas of molecular …

Question

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A thermally insulated vessel contains an ideal gas of molecular mass

M

and ratio of specific heats

γ .

It is moving with speed

v

and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

Accepted Answer

Here, work done is zero.
So, loss in kinetic energy

=

change in internal energy of gas

\frac{1}{2} m v^{2} = n C_{v} Δ T = n \frac{R}{γ - 1} Δ T

\frac{1}{2} m v^{2} = \frac{m}{M} \frac{R}{γ - 1} Δ T

∴

Δ T = \frac{M v^{2} (γ - 1)}{2 R} K

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