At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperatur

step 1 In this problem, temperature is given as minus 56 .5 degrees centigrade which is equal to minus

At an altitude of 11,000 m (a typical cruising altitude for...

At an altitude of $11,000 \mathrm{~m}$ (a typical cruising altitude for a jet airliner), the air temperature is $-56.5^{\circ} \mathrm{C}$ and the air density is $0.364 \mathrm{~kg} / \mathrm{m}^{3} .$ What is the pressure of the atmosphere at that altitude? The molar mass of air is $28.8 \mathrm{~g} / \mathrm{mol}$.

Key Concepts

Atmospheric Pressure and Altitude

Atmospheric pressure is the force per unit area exerted by the weight of the air above. At higher altitudes, reduced air density and lower temperatures contribute to a decrease in pressure, a concept that is essential in understanding atmospheric phenomena.

Molar Mass and Gas Constants

Molar mass connects the mass of the gas to the number of moles, and when used with the universal gas constant (R), it provides a means to relate microscopic molecular behavior to macroscopic properties like pressure and density.

Relationship between Density and Pressure

The density of a gas is intrinsically linked to its pressure, temperature, and molar mass via the ideal gas law. This relationship allows for the calculation of one variable if the others are known, making it fundamental in studies of atmospheric conditions.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle in thermodynamics that relates the pressure, volume, temperature, and amount of a gas. It enables the prediction of one property of a gas when the others are known and is crucial for calculating atmospheric conditions.

Temperature Conversion to Kelvin

Accurate gas law calculations require temperatures to be in absolute terms (Kelvin). Converting from Celsius to Kelvin ensures that the values used are compatible with the ideal gas law, as it depends on the absolute temperature scale.

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