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A massless closed adiabatic vessel contains $n$ moles of monatomic gas with atomic weight $M$ . The vessel is kept on a vehicle moving horizontally with speed $v$ . When the vehicle stops suddenly, ( $R$ = universal gas constant)

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Increase in temperature of the gas is $\frac{M V^{2}}{3 R}$

Fractional increase in pressure is equal to fractional increase in temperature

The increase in temperature is independent of the number of moles

Increase in temperature of the gas is $\frac{M V^{2}}{2 R}$

answer is A, C, D.

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Detailed Solution

$\frac{1}{2} (n M) v^{2} = n (\frac{3}{2} R) Δ T ∴ Δ T = \frac{M v^{2}}{3 R} P v = n R T ∴ \frac{Δ P}{P} = \frac{Δ T}{T}$

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