Calculate the predicted viscosity of molecular oxygen, nitrogen and methane at 20°C
and standard atmospheric pressure (give your answer in Pas).
To calculate the predicted viscosity of gases like molecular oxygen, nitrogen, and methane at a specific temperature and pressure, we can use the Sutherland's formula.
Sutherland's formula relates the viscosity of a gas to its temperature and molecular properties. The equation is given as:
μ = (μ₀ * T₀) / (T + S)
where:
μ = viscosity of the gas at the desired temperature and pressure
μ₀ = viscosity of the gas at reference temperature T₀
T₀ = reference temperature (usually set as 273.15 K or 0°C)
T = desired temperature in Kelvin
S = Sutherland's constant (unique for each gas)
We need to find the Sutherland's constant (S) for each gas first:
For molecular oxygen (O2):
S = 127.0 K
For nitrogen (N2):
S = 111.0 K
For methane (CH4):
S = 155.0 K
Now, let's calculate the viscosity for each gas using the given formula and the temperature of 20°C (293.15 K) and standard atmospheric pressure (~1 atm):
For O2:
μ = (μ₀ * T₀) / (T + S) = (0.02197 * 273.15) / (293.15 + 127.0) = 0.01895 Pa·s
For N2:
μ = (μ₀ * T₀) / (T + S) = (0.01846 * 273.15) / (293.15 + 111.0) = 0.01607 Pa·s
For CH4:
μ = (μ₀ * T₀) / (T + S) = (0.01295 * 273.15) / (293.15 + 155.0) = 0.01046 Pa·s
Therefore, the predicted viscosities of molecular oxygen, nitrogen, and methane at 20°C and standard atmospheric pressure are:
Oxygen (O2): 0.01895 Pa·s
Nitrogen (N2): 0.01607 Pa·s
Methane (CH4): 0.01046 Pa·s