atmospheric pressure decreases by about 12% for every 1000 meters you climb. The pressure at sea level is about 1.013 atmospheres. Construct a model to represent the atmospheric pressure at a given altitude in thousands of meters
That would, of course, be
P(h) = 1.013 * 0.88^x
where x is in thousands of meters
For every 1000 m of ascent,the temperature decreases by 6 degree celsius
To construct a model representing the atmospheric pressure at a given altitude in thousands of meters, we can use the following formula:
Pressure = 1.013 * (0.88)^n
Where:
- Pressure represents the atmospheric pressure at the given altitude.
- 1.013 is the pressure at sea level in atmospheres.
- 0.88 is the factor by which the pressure decreases for every 1000 meters climbed.
- n represents the number of thousands of meters above sea level.
By plugging in the value of n, which represents the altitude in thousands of meters, into this formula, we can calculate the atmospheric pressure at that altitude.
To construct a model to represent the atmospheric pressure at a given altitude in thousands of meters, we can use the information provided: the atmospheric pressure decreases by about 12% for every 1000 meters climbed, and the pressure at sea level is about 1.013 atmospheres.
Let's start by defining some variables:
- P: Atmospheric pressure at a given altitude in atmospheres
- h: Altitude in thousands of meters
Using the information given, we can establish the following relationship:
For every 1000 meters climbed (or h = 1), the atmospheric pressure decreases by 12%.
From this, we can create a formula to calculate the atmospheric pressure at any given altitude:
P = 1.013 * (0.88^h)
Explanation:
- We start with the pressure at sea level, 1.013 atmospheres.
- To calculate the pressure at a given altitude in thousands of meters, we multiply the initial pressure by the reduction factor, which is 0.88 raised to the power of the altitude in thousands of meters.
For example, if we want to know the atmospheric pressure at an altitude of 3,000 meters, we substitute h = 3 into the formula:
P = 1.013 * (0.88^3)
P = 1.013 * 0.681472
P ≈ 0.691 atmospheres
So, according to the model, the atmospheric pressure at an altitude of 3,000 meters would be approximately 0.691 atmospheres.