Question

By how many folds the temperature of a gas would increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from 5 × 10⁴ cm/s to 10 × 10⁴ cm/s?

Options

• Two

• Three

• Six

• Four

Answer 1

Four

Explanation:

r.m.s. velocity V_rms = `sqrt((3"RT")/"M")`

i.e., `"V"_1/"V"_2 = sqrt("T"_1/"T"_2)`

`(5 xx 10^4)/(10 xx 10^4) = sqrt("T"_1/"T"_2)`

`1/2 = sqrt("T"_1/"T"_2)`

∴ T₂ = 4T₁