Question

Альпинисты поднялись на гору высотой 5100 м,у подножия горы давление было 720 мм ртутного столба.Какое давление будет на вершине горы?

Answer 1

При подъеме на 10,5 м атмосферное давление понижается на 1 мм рт. ст.
1) 5100 : 10,5 = 486
2) 720 - 486 = 234 мм рт. ст.
Ответ: 234 мм рт. ст.

Answer 2

Calculating Pressure at the Mountain Summit

To calculate the pressure at the summit of the mountain, we can use the barometric formula, which describes how the pressure of the atmosphere decreases with altitude. The formula is given by:

P = P₀ * e^(-Mgh/RT)

Where: - P is the pressure at the summit - P₀ is the pressure at the base of the mountain - M is the molar mass of Earth's air - g is the acceleration due to gravity - h is the height difference between the base and the summit - R is the universal gas constant - T is the average temperature of the atmosphere

Applying the Barometric Formula

Given: - Height of the mountain, h = 5100 m - Pressure at the base of the mountain, P₀ = 720 mmHg

We can use the barometric formula to calculate the pressure at the summit of the mountain.

Using the barometric formula: P = P₀ * e^(-Mgh/RT)

Let's calculate the pressure at the summit using the given values.

Calculation

Using the given values and assuming standard atmospheric conditions: - M (molar mass of Earth's air) is approximately 0.029 kg/mol - g (acceleration due to gravity) is approximately 9.81 m/s² - R (universal gas constant) is approximately 8.314 J/(mol·K) - T (average temperature of the atmosphere) is approximately 288 K

Plugging in the values: P = 720 mmHg * e^(-0.029*9.81*5100/(8.314*288))

Calculating the value: P ≈ 720 mmHg * e^(-15.09)

Using the exponential function: P ≈ 720 mmHg * 3.35 x 10^-7

Result

The pressure at the summit of the mountain is approximately 0.000241 mmHg.