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Question:

The molecules of a given mass of a gas have r.m.s velocity of 200 m/s at 270°C and 1.0 × 10⁵ Nm⁻² pressure. When the temperature and pressure of the gas are respectively, 1270°C and 0.05 × 10⁵ Nm⁻², the r.m.s. velocity of its molecules in m/s is:

100√23

100√3

100√2

400√3

Solution:

We know that:
v ∝ √T
=> v/200 = √(400/300)
=> v = 200 × 2√3 = 400√3 m/s