The molecules of a given mass of a gas have r.m.s. velocity of 200 ms⁻¹ at 27°C and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 × 10⁵ Nm⁻², the r.m.s. velocity of its molecules in ms⁻¹ is:

Question

Accepted Answer

100√2. The r.m.s. velocity of gas molecules is proportional to the square root of the absolute temperature (T) and independent of pressure. Converting temperatures to Kelvin: T₁ = 27°C + 273 = 300 K, T₂ = 127°C + 273 = 400 K. Using the relation v₂/v₁ = √(T₂/T₁), we get v₂ = 200 × √(400/300) = 200 × √(4/3) = 100√2 ms⁻¹.

The molecules of a given mass of a gas have r.m.s. velocity of 200 ms⁻¹ at 27°C and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 × 10⁵ Nm⁻², the r.m.s. velocity of its molecules in ms⁻¹ is:

Solution

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