Question

The molecular velocities of two gases at the same temperature
are u₁ and u2. Their masses are m1 and m2 respectively .
Which of the following expression is correct.
(a) m₁ / u₁² = m₂ / u₂² (b) m₁u₁ = m₂u₂
(c) m₁ / u₁ = m₂ / u₂ (d) m₁u₁² = m₂ u₂²

Answer 1

The correct expression is m1u1^2 = m2u2^2

Option (D) is correct.

Explanation:

U(rms) = √3RT / M

Lets say we have two gases A and B.

For gas A:

Molecular mass = m1

Molecular velocity = u1

u1 = √3RT / m1

For gas B:

Molecular mass = m2

Molecular velocity = u2

From equation (1)

3RT / M1 = u1^2

T = m1u1^2 / 3R   -----(1)

From equation (2)

3RT / m2 = u2^2

T = m2u2^2 / 3R ----(2)

From equation (1) and (2)

m1u1^2 / 3R  =  m2u2^2 / 3R

m1u1^2 = m2u2^2

Thus the correct expression is m1u1^2 = m2u2^2

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