Question

The root-mean-square speed (thermal speed) of the molecules of a gas is 200m/s at 23.0°C. At 227°C the root-mean-square speed (thermal speed) of the molecules will be closest to (1) 160 m/s. (2) 330 m/s. (3) 260 m/s. (4) 630 m/s. (5) None of the above.

Answer 1

Answer:

330 m/s  approx

Explanation:

The RMS speed of a gas is proportional to square root of its absolute temperature is

V ( RMS ) ∝ √T

$\frac{V_1}{V_2} =\sqrt{\frac{T_1}{T_2} }$

Here V₁ = 200 , T₁ = 23 +273 = 300K , T₂ = 227 +273 = 500 K

Putting the values

200 / V₂ = $\sqrt{\frac{300}{500} }$

V₂ = 330 m/s  approx