A thermally insulated vessel containing an ideal gas ( M = 4 ) at a temperature t = 2 7 ∘ C moves with velocity v = 100 m s − 1 . How much (in per cent) will the gas pressure change on a sudden stoppage of the vessel?

The gas is monoatomic ( M = 4 , helium), γ = 3 5 . Δ T = 2 R M v 2 ( γ − 1 ) = 2 × 8.314 0.004 × 1 0 4 × 3 2 = 1.60 K. At constant volume P Δ P = T Δ T = 300 1.60 = 0.54% .

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PhysicsHeat & ThermoThermodynamics Laws & Specific Heats of GasesMedium2 minQB

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A thermally insulated vessel containing an ideal gas ( $M = 4$ ) at a temperature $t = 2 7^{\circ}$ C moves with velocity $v = 100$ m $s^{- 1}$ . How much (in per cent) will the gas pressure change on a sudden stoppage of the vessel?

Answer:

0.54

Solution:

The gas is monoatomic ( $M = 4$ , helium), $γ = \frac{5}{3}$ . $Δ T = \frac{M v ^{2} ( γ - 1 )}{2 R} = \frac{0.004 \times 1 0 ^{4} \times \frac{2}{3}}{2 \times 8.314} = 1.60$ K. At constant volume $\frac{Δ P}{P} = \frac{Δ T}{T} = \frac{1.60}{300} = 0.54%$ .

Subject:PhysicsTopic:Heat & ThermoSubtopic:Thermodynamics Laws & Specific Heats of Gases

⏱ 2mℹ️ Source: QB

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