Many people know that with increasing height, air pressure decreases. Consider the question of why air pressure decreases with height, we give a formula for the dependence of pressure on height, and also consider an example of solving the problem using the obtained formula.
What is air?
Air is a colorless mixture of gases that makes up the atmosphere of our planet. It consists of many different gases, the main of which are nitrogen (78%), oxygen (21%), argon (0.9%), carbon dioxide (0.03%) and others.
From the point of view of physics, the behavior of air under existing conditions on Earth obeys the laws of an ideal gas - a model according to which the molecules and atoms of the gas do not interact with each other, the distances between them are huge compared to their sizes, and the speed of movement at room temperature is about 1000 m /with.
Air pressure
Considering the question of the dependence of pressure on height, it is necessary to understand what the concept of "pressure" is from a physical point of view. By air pressure is meant the force with which the air column presses on the surface. In physics, it is measured in pascals (Pa). 1 Pa means that a force of 1 newton (N) is applied perpendicularly to a surface of 1 m 2 . Thus, a pressure of 1 Pa is a very small pressure.
At sea level, the air pressure is 101 325 Pa. Or, rounding, 0.1 MPa. This value is called the pressure of 1 atmosphere. The above figure says that air presses with a force of 100 kN on a 1 m 2 platform! This is a great force, but a person does not feel it, since inside it the blood creates a similar pressure. In addition, air is a fluid substance (also liquid). And this means that he exerts the same pressure in all directions. The latter fact suggests that the pressure of the atmosphere from different sides on a person is mutually compensated.
Pressure Dependence on Height
The atmosphere around our planet is held by Earth's gravity. Gravitational forces are also responsible for the drop in air pressure with increasing altitude. In fairness, it should be noted that not only gravity leads to a decrease in pressure. And also a decrease in temperature also contributes.
Since air is a fluid substance, then it is possible to use the hydrostatic formula for the dependence of pressure on depth (height), that is, ฮP = ฯ * g * ฮh, where: ฮP is the pressure change when the height changes by ฮh, ฯ is the air density, g - acceleration of gravity.
Considering that air is an ideal gas, it follows from the equation of state of an ideal gas that ฯ = P * m / (k * T), where m is the mass of 1 molecule, T is its temperature, and k is the Boltzmann constant.
Combining the two above formulas and solving the equation with respect to pressure and height, we can obtain the following formula: P h = P 0 * e -m * g * h / (k * T) , where P h and P 0 are the pressure at a height h and at sea level, respectively. The resulting expression is called the barometric formula. It can be used to calculate the dependence of atmospheric pressure on altitude.
Sometimes for practical purposes it is necessary to solve the inverse problem, that is, find the height, knowing the pressure. From the barometric formula, one can easily obtain the dependence of the height on the pressure level: h = k * T * ln (P 0 / P h ) / (m * g).
Problem solving example
The Bolivian city of La Paz is the tallest capital in the world. From various sources it follows that the city is located at an altitude of 3250 meters to 3700 meters above sea level. The task is to calculate the air pressure at the height of La Paz.
To solve the problem, we use the formula for the dependence of pressure on height: P h = P 0 * e -m * g * h / (k * T) , where: P 0 = 101 325 Pa, g = 9.8 m / s 2 , k = 1.38 * 10 -23 J / K, T = 293 K (20 o C), h = 3475 m (average between 3250 m and 3700 m), m = 4.817 * 10 -26 kg (taking into account the molar mass of air 29 g / mol). Substituting the numbers, we obtain: P h = 67 534 Pa.
Thus, the air pressure in the capital of Bolivia is 67% of the sea level pressure. Low air pressure causes dizziness and general weakness of the body when a person rises to mountainous areas.