JEE Main 2023 · 6 April · evening · Single correct · +4 / −1
The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is v₀. Then, r.m.s. speed of the gas at 800 K will be:
- (a) v₀
- (b) 2 v₀
- (c) 4 v₀
- (d) v₀/4
Answer and solution
Answer (b) 2 v₀
Solution
Physics sir · 3 steps
The rms speed goes as the square root of T, so four times the temperature only doubles the speed.
- Rms speed formula. For an ideal gas of molar mass M, the rms speed depends only on temperature. The gas is the same, so M does not change.
vᵣₘₛ = √(3RT/M) ⇒ vᵣₘₛ ∝ √T
- Take the ratio. v₈₀₀/v₂₀₀ = √(800/200) = √4 = 2.
- So. The rms speed at 800 K is 2v₀, option (b).
The idea to keep. Rms, average and most probable speeds all go as √(T/M). Take the ratio of temperatures first, then the square root.
Answer from the NTA final answer key. Solution by PrepWiser.