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benitta
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how does the speed of sound vary with temperature in an ideal gas? how do we derive this relation?
The speed of sound in an ideal gas is given by the formula:
c = √(γRT)
where c is the speed of sound, γ is the ratio of specific heats, R is the gas constant, and T is the temperature in Kelvin.
According to the formula c = √(γRT), the speed of sound in an ideal gas is directly proportional to the square root of temperature. This means that as temperature increases, so does the speed of sound.
The speed of sound in an ideal gas can be derived using the ideal gas law, the adiabatic equation of state, and the conservation of energy equation. A detailed derivation involves solving for the speed of sound in terms of pressure, density, and specific heat ratio.
According to the formula c = √(γRT), the speed of sound in an ideal gas is directly proportional to the square root of pressure. This means that as pressure increases, so does the speed of sound.
The speed of sound in an ideal gas is an important parameter in understanding the behavior of gases and their interactions with each other. It is also used in various engineering applications, such as designing aircrafts and predicting the behavior of sound waves in different environments.