Question

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 600K?​

Answer 1

Answer:

The RMS speed of the gas molecule at 600k is = 565.68 m/s.

Explanation:

We know the formulae that the RMS speed of a molecule

$V_{RMS} = \sqrt{\frac{3RT}{M} } -----------------(1)$

Where R = ideal gas constant.

T = the temperature of the gas.

and M = the mass of the gas molecule.

Now, if the temperature is doubled (i.e. 300k to 600k ) then using eq(1)-

$V_{1} = \sqrt{\frac{3R*300}{M} } = 400 m/s$

Where  V₁ is the initial RMS speed of the molecule (at 300k).

Now,

$V_2 = \sqrt{\frac{3R* 600}{M} } = \sqrt{2} V_1= 1.412 \times400= 565.68$

Therefore, the RMS speed of the gas molecule at 600k is = 565.68 m/s.