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Chapter 5: Problem 2

Compute the velocity of sound in hydrogen, the lightest gas, and in UF \(_{6}\), a heavy gas, both at standard conditions. Assume \(\gamma=1.3\) for the latter gas.

Short Answer

Expert verified
Answer: The velocities of sound in hydrogen and UF6 gases under standard conditions are approximately 113.92 m/s and 16.08 m/s, respectively.

Step by step solution

01

Formula for the speed of sound

The formula to compute the speed of sound (\(v\)) in a gas is given by: \(v = \sqrt{\gamma R T / M}\) where \(\gamma\) is the adiabatic index, \(R\) is the ideal gas constant, \(M\) is the molar mass of the gas, and \(T\) is the temperature. Step 2: Constants and values for hydrogen
02

Constants and values for hydrogen

For hydrogen, we have the following values: - Molar mass: \(M_H = 2.016 \times 10^{-3} kg/mol\) - Adiabatic index: \(\gamma_H = 1.4\) - Ideal gas constant: \(R = 8.314 J/(mol\cdot K)\) - Standard temperature: \(T = 273.15 K\) Step 3: Compute the velocity of sound in hydrogen
03

Compute the velocity of sound in hydrogen

Using the formula from Step 1 and the values from Step 2, we can compute the velocity of sound in hydrogen: \(v_H = \sqrt{\frac{1.4 \times 8.314 \times 273.15}{2.016 \times 10^{-3}}}\) \(v_H = \sqrt{12978.16}=113.92 m/s\) Step 4: Constants and values for UF\(_6\)
04

Constants and values for UF\(_6\)

For UF\(_6\), we have the following values: - Molar mass: \(M_{UF_{6}} = 352 \times 10^{-3} kg/mol\) - Adiabatic index: \(\gamma = 1.3\) - Ideal gas constant: \(R = 8.314 J/(mol\cdot K)\) - Standard temperature: \(T = 273.15 K\) Step 5: Compute the velocity of sound in UF\(_6\)
05

Compute the velocity of sound in UF\(_6\)

Using the formula from Step 1 and the values from Step 4, we can compute the velocity of sound in UF\(_6\): \(v_{UF_{6}} = \sqrt{\frac{1.3 \times 8.314 \times 273.15}{352 \times 10^{-3}}}\) \(v_{UF_{6}} = \sqrt{258.55}=16.08 m/s\) The velocities of sound in hydrogen and UF\(_6\) gases under standard conditions are approximately 113.92 m/s and 16.08 m/s, respectively.

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