Question

Two gases A and B are at absolute temperatures of 360 K and 420 K, respectively. The ratio of the average kinetic energy of the molecules of gas B to that of gas A is ______.

Options

• 6 : 7

• 49 : 36

• `sqrt7 : sqrt6`

• 7 : 6

Answer 1

Two gases A and B are at absolute temperatures of 360 K and 420 K, respectively. The ratio of the average kinetic energy of the molecules of gas B to that of gas A is 7 : 6.

Explanation:

For kinetic energy,

KE = `3/2kT`

KE ∝ T ⇒ `(KE_A)/(KE_B) = T_A/T_B`

Given, T₁ = 360 K, T₂ = 420 K

`(KE_B)/(KE_A) = T_B/T_A = 420/360`

∴ `(KE_B)/(KE_A) = 7/6`

Hence, KE_B : KE_A = 7 : 6