Question

Which of the following expression can be used to express the relationship between root mean square velocity (v) of two ideal gases A and B and temperature (T) for the given mass? (d is constant)
1. V = d T
2. V ​= d T ^-1
3. V = d T ^-2
4. v = d √ T

Answer 1

Correct Answer - Option 4 : v = d √ T

CONCEPT:

• Root Mean Square Speed of Gas (RMS) is defined as the square root of the mean of squares of the speed of different molecules.
• Molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
• The root mean square velocity of the ideal gas is given as

 \(V_{rms} = √{\frac{3RT}{M}}\)

k is the Boltzmann constant, m is the mass of the Gas, T is temperature

EXPLANATION:

In the expression for the root mean square velocity, k is constant, 

mass m is constant according to the question. 

So,

\(V_{rms} = √{\frac{3R}{M}}.√{T}\)

⇒ V_rms = (constant) . √ T

So, we can replace constant by d

⇒ Vrms = d. √ T

So, root mean square velocity, in this case, can be represented as

v = d. √ T