Chapter 19, Problem 19.31E

Interpretation Introduction

(a)

Interpretation:

The specific value for ${\nu }_{\text{sound}}$ for a monatomic ideal gas at $298\text{K}$ is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different velocity. The speed of sound in a gas is less than the speed of sound in vacuum. The speed of sound in a gas, ${\nu }_{\text{sound}}$, is given by the expression

${\nu }_{\text{sound}}={\left(\frac{\gamma RT}{M}\right)}^{1/2}$ …(2)

Where,

• $R$ represents the gas constant with a value of $8.314\text{J}/\text{K}\cdot \text{mol}$.

• $T$ represent the temperature of the gas.

• $M$ represents the molar mass of the gas.

• $\gamma$ represents the ratio of heat capacity at constant pressure and heat capacity at constant volume.

Interpretation Introduction

(b)

Interpretation:

The value of ${\nu }_{\text{sound}}$ for $\text{He}$ at $273\text{K}$ is to be determined.

Concept introduction:

A gas is made up of many atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.