Question

(Std. 12th phy.3)
iii) The rms speed of molecules of a certain gas at 300K is 400 m/s. What
will be the rms speed, if the gas is heated to 600 K.

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Answer 1

Given info : The rms speed of molecules of a certain gas at 300 K is 400 m/s.

To find : what will be the RMS speed, if the gas is heated to 600K.

solution : RMS speed of an ideal gas is given by, v = √{3RT/M}

here you see, RMS speed is directly proportional to square root of temperature.

i.e., v ∝ √T

⇒v₁/v₂ = √(T₁/T₂)

here, v₁ = 400 m/s, v₂ = ? , T₁ = 300K , T₂ = 600K

so 400/v₂ = √(300/600) = 1/√2

⇒v₂ = 400√2 = 400 × 1.414 = 565.6 m/s

Therefore the rms speed of gas will be 565.6 m/s if it is heated to 600K.