The speed of a sound in a container of hydrogen at 201 K is...

The speed of a sound in a container of hydrogen at $201 \mathrm{~K}$ is $1220 \mathrm{~m} / \mathrm{s}$. What would be the speed of sound if the temperature were raised to $405 \mathrm{~K}$ ? Assume that hydrogen behaves like an ideal gas.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Speed of Sound in an Ideal Gas

This concept explains that the speed of sound in a gas is influenced by properties such as the ratio of specific heats (?), the universal gas constant (R), the absolute temperature (T), and the molar mass (M) of the gas. The relationship is commonly expressed as v = ?(?RT/M), indicating that, for an ideal gas, the speed of sound increases as the square root of the temperature.

Ideal Gas Behavior

This concept involves understanding how gases behave under the ideal gas assumption, where intermolecular forces and the volume of molecules are negligible. By applying the ideal gas law (PV = nRT), one can derive relationships that simplify the analysis of thermodynamic properties, such as the dependence of sound speed on temperature.

Temperature Dependence

This concept focuses on the relationship between temperature and kinetic energy in a gas. As the temperature increases, the average kinetic energy of the gas molecules increases, leading to an increase in the speed at which sound propagates. This is mathematically represented by a proportionality to the square root of the temperature, namely, v ? ?T.

Transcript

Please give Ace some feedback