constant gamma(Y) for the oxygen as well as for hydrogen is 1.40. If the speed of the oxygen is 460 m/s, what will be the speed of the sound in hydrogen at same temperature and pressure
Solve the problem
To find the speed of sound in hydrogen at the same temperature and pressure, we can use the relationship between the speed of sound, the molar mass, and the ratio of specific heats. The formula is:
v = sqrt((γ * R * T) / M)
where:
v is the speed of sound,
γ is the ratio of specific heats,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin,
and M is the molar mass of the gas.
Given that γ for hydrogen is also 1.40, we can substitute the values into the formula:
Molecular mass of oxygen (O2) = 32 g/mol
Molecular mass of hydrogen (H2) = 2 g/mol
Speed of oxygen (v_oxygen) = 460 m/s
We can calculate the speed of sound in hydrogen as follows:
v_hydrogen = sqrt((γ_hydrogen * R * T) / M_hydrogen)
Since we are assuming the same temperature and pressure, we don't need to consider those parameters for this calculation.
v_hydrogen = sqrt((γ_hydrogen * R) / M_hydrogen)
v_hydrogen = sqrt((1.40 * 8.314 J/(mol·K)) / 2 g/mol)
v_hydrogen = sqrt(11.6312 J/(mol·K* g/mol))
v_hydrogen = sqrt(11.6312 J/(K·g))
Simplifying further, we find:
v_hydrogen = sqrt(11.6312) m/s
v_hydrogen ≈ 3.41 m/s
Therefore, the speed of sound in hydrogen, at the same temperature and pressure, is approximately 3.41 m/s.