Two vessels of the same volume are filled with the same gas at the sam

1.	Two vessels of the same volume are filled with the same gas at the same temperature. if the pressure of the gas in these vessels be in the ratio of 1 : 2, then state (i) The ratio of r.m.s. speeds of the molecules, (ii) The ratio of number of molecules.
Answer» As, \(P=\frac{1}{3}\frac{mnc^2}{V}\), so P ∝ nc² (i) Here, M and V are constant. Since c ∝ \(\sqrt{T}\) But, T is constant So, c₁: c₂ = 1 : 1 (ii) When temperature is same for two vessels then, P ∝ n. i.e., \(\frac{n_1}{n_2}=\frac{P_1}{P_2}=\frac{1}{2}\)

Two vessels of the same volume are filled with the same gas at the same temperature. if the pressure of the gas in these vessels be in the ratio of 1 : 2, then state (i) The ratio of r.m.s. speeds of the molecules, (ii) The ratio of number of molecules.

Answer»

As,

\(P=\frac{1}{3}\frac{mnc^2}{V}\),

so P ∝ nc²

(i) Here, M and V are constant.

Since c ∝ \(\sqrt{T}\)

But, T is constant

So, c₁: c₂ = 1 : 1

(ii) When temperature is same for two vessels then,

P ∝ n.

i.e., \(\frac{n_1}{n_2}=\frac{P_1}{P_2}=\frac{1}{2}\)

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Two vessels of the same volume are filled with the same gas at the same temperature. if the pressure of the gas in these vessels be in the ratio of 1 : 2, then state (i) The ratio of r.m.s. speeds of the molecules, (ii) The ratio of number of molecules.

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