Two monoatomic ideal gases 1 and 2 has molecular weights m1 and m2. Both are kept in two differe

step 1 In this question, we will learn about some basic concept of the oscillation and waves. The quest

Two monoatomic ideal gases 1 and 2 has molecular weights m1...

Two monoatomic ideal gases 1 and 2 has molecular weights $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$. Both are kept in two different containers at the same temperature. The ratio of velocity of sound wave in gas 1 and 2 is $\ldots \ldots \ldots$ (A) $\sqrt{\left(m_{2} / m_{1}\right)}$ (B) $\sqrt{\left(m_{1} / m_{2}\right)}$ (C) $\left(\mathrm{m}_{1} / \mathrm{m}_{2}\right)$ (D) $\left(\mathrm{m}_{2} / \mathrm{m}_{1}\right)$

Two monoatomic ideal gases 1 and 2 has molecular weights $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$. Both are kept in two different containers at the same temperature. The ratio of velocity of sound wave in gas 1 and 2 is $\ldots \ldots \ldots$
(A) $\sqrt{\left(m_{2} / m_{1}\right)}$
(B) $\sqrt{\left(m_{1} / m_{2}\right)}$
(C) $\left(\mathrm{m}_{1} / \mathrm{m}_{2}\right)$
(D) $\left(\mathrm{m}_{2} / \mathrm{m}_{1}\right)$

Key Concepts

Monoatomic Gases

Monoatomic gases consist of single atoms and represent a simplified case in thermodynamics where the heat capacity and energy distribution follow straightforward rules compared to more complex molecular gases. Their simplicity allows for more direct application of theoretical models like the ideal gas law and expressions for the speed of sound, making them useful in deriving fundamental physical relationships.

Molecular Weight

Molecular weight, or molar mass, is a key property of a gas that affects its dynamic behavior, especially in the context of kinetic theory and thermodynamics. It appears in various equations, including those for the speed of sound and energy distribution, influencing how quickly molecules move and interact. In gas dynamics, variations in molecular weight lead to measurable differences in phenomena such as diffusion and acoustic propagation.

Ideal Gas Law

The ideal gas law relates the pressure, volume, and temperature of an ideal gas, providing a simplified model that assumes no interactions between particles apart from elastic collisions. This law underpins many fundamental derivations in gas dynamics, including calculations for how pressure and temperature affect various properties such as speed and energy distribution in gases.

Speed of Sound in Gases

The speed of sound in a gas is determined by how quickly pressure disturbances propagate through the medium. It is given by the formula c = ?(?RT/M), where ? is the adiabatic index, R is the gas constant, T is the absolute temperature, and M is the molar mass. This relationship shows that the speed of sound is not only dependent on temperature but also inversely related to the square root of the molecular weight, which is essential in comparing different gases.

Transcript

Please give Ace some feedback