To derive an expression for the speed of sound based on van der Walls’s equation of state
Answer to Problem 122RP
The speed of sound in carbon dioxide by using the relation obtained from the van der Walls equation is
The speed of sound in carbon dioxide by assuming as ideal gas is
Explanation of Solution
Write the given equation of state.
Here, the pressure is
Partially differentiate the Equation (I) with respect to specific volume
Write the relation of speed of the sound.
Here, the specific heat ratio is
Write the relation between density and specific volume.
Partially differentiate the
Substitute
Substitute
Write the formula for velocity of sound at the given conditions of
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The molar mass
The gas constant
Refer Table A-2, “Ideal-gas specific heats of various common gases”.
The specific heat ratio
Conclusion:
Express the van der Walls constant
Substitute
By using Equation solver or online calculator solve the Equation (VII) and the value of
Substitute
Thus, the speed of sound in carbon dioxide by using the relation obtained from the van der Walls equation is
When the carbon dioxide is assumed as ideal gas, the velocity of sound is determined as follows.
Substitute
Thus, the speed of sound in carbon dioxide by assuming as ideal gas is
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Chapter 17 Solutions
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