If the mass of 1 mole of air is 29 ×10^-3 kg, then the speed of sound in it at STP is (γ=7 / 5)

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

If the mass of 1 mole of air is 29 ×10^-3 kg, then the...

If the mass of 1 mole of air is $29 \times 10^{-3} \mathrm{~kg}$, then the speed of sound in it at STP is $(\gamma=7 / 5) .\left\{\mathrm{T}=273 \mathrm{~K}, \mathrm{P}=1.01 \times 10^{5} \mathrm{~Pa}\right\}$ (A) $270 \mathrm{~m} / \mathrm{s}$ (B) $290 \mathrm{~m} / \mathrm{s}$ (C) $330 \mathrm{~m} / \mathrm{s}$ (D) $350 \mathrm{~m} / \mathrm{s}$

If the mass of 1 mole of air is $29 \times 10^{-3} \mathrm{~kg}$, then the speed of sound in it at STP is $(\gamma=7 / 5) .\left\{\mathrm{T}=273 \mathrm{~K}, \mathrm{P}=1.01 \times 10^{5} \mathrm{~Pa}\right\}$
(A) $270 \mathrm{~m} / \mathrm{s}$
(B) $290 \mathrm{~m} / \mathrm{s}$
(C) $330 \mathrm{~m} / \mathrm{s}$
(D) $350 \mathrm{~m} / \mathrm{s}$

Key Concepts

Speed of Sound in Gases

The speed of sound in gases is derived from the relationship between the pressure forces that restore equilibrium and the inertia of the gas. It is determined by factors such as the temperature and the molecular composition of the gas. Mathematically, it is expressed as the square root of the product of the adiabatic index and the specific gas constant times the temperature, emphasizing that sound propagates faster in warmer gases due to increased molecular motion.

Adiabatic Index (?)

The adiabatic index, often denoted as ?, is the ratio of specific heats at constant pressure and constant volume (Cp/Cv). This parameter is crucial in adiabatic processes, where no heat is exchanged with the surroundings, and it directly influences the speed of sound in the medium by representing the stiffness of the gas in response to compression.

Ideal Gas Law

The Ideal Gas Law provides a relationship among pressure, volume, temperature, and the number of moles of a gas. This law helps in connecting macroscopic thermodynamic properties with molecular behavior. In the context of sound propagation, it is used to derive expressions for density and the specific gas constant based on temperature and pressure, which are essential in calculating the speed of sound.

Specific Gas Constant

The specific gas constant is derived by dividing the universal gas constant by the molar mass of the gas. It appears in formulas that describe the behavior of gases, such as the ideal gas law and the equation for the speed of sound. This constant allows the translation of properties on a per-mass basis, which is vital for computing thermodynamic characteristics and acoustic properties of a gas.

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