Question

Mean free path of O2 gas molecules in rigid container is (lamada). The temperature of gas is doubled, then new mean free path of O2 gas molecules is​

Answer 1

Explanation:

• lamada is inversely proportional to temperature

When temp increases by 2 , lambda decreases by 2

Answer 2

Given : Mean free path of O₂ gas molecules in rigid container is λ.

To find : The Temperature of gas is doubled, then new mean free path of O₂ gas ...

Solution : The mean free path is given by equation,

$\lambda=\frac{1}{\sqrt{2}\pi d^2\left(\frac{N}{V}\right)}$.......(1)

where d is diameter of gaseous molecule, N is number of collisions and V is volume of container.

As it is given that, container is rigid. means, volume of gaseous molecules remains same when temperature is doubled.

at constant volume , mean free path doesn't depend on temperature. as you can see T doesn't appear in equation (1).

as the temperature is increased, molecules are moving faster but the average distance between them is not affected. it's true that the mean time between collisions decreases but the mean distance travelled between collisions remains same.

so, mean free path remains constant.

Therefore new mean free path of O₂ gas molecules is λ.

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