Question

На дне шахты барометр зафиксировал 780 мм рт. ст. На поверхности земли 760 мм рт. ст. Найти глубину шахты.

Answer 1

1) 200 : 10,5 + 752 = 771,05771,05 мм рт.ст. 2) (780 - 760) х 10,5 = 210 м

Answer 2

Calculation of the Depth of the Mine

To calculate the depth of the mine, we can use the difference in atmospheric pressure between the surface and the bottom of the mine. The atmospheric pressure decreases with increasing altitude, so the pressure at the bottom of the mine will be higher than at the surface.

Given that the barometer at the bottom of the mine recorded a pressure of 780 mmHg (millimeters of mercury) and the barometer at the surface recorded a pressure of 760 mmHg, we can calculate the difference in pressure.

The difference in pressure between the bottom and the surface is equal to the weight of the column of air above the mine. This can be calculated using the equation:

ΔP = ρgh

Where: - ΔP is the difference in pressure - ρ is the density of air - g is the acceleration due to gravity - h is the height of the column of air

Since we are given the pressure in mmHg, we need to convert it to pascals (Pa) before performing the calculation. 1 mmHg is equal to 133.322 Pa.

Let's calculate the depth of the mine using the given information:

1. Convert the pressure from mmHg to Pa: - Pressure at the bottom of the mine: 780 mmHg = 780 * 133.322 Pa = 103,993.16 Pa - Pressure at the surface: 760 mmHg = 760 * 133.322 Pa = 101,325.92 Pa

2. Calculate the difference in pressure: - ΔP = 103,993.16 Pa - 101,325.92 Pa = 2,667.24 Pa

3. Calculate the depth of the mine: - ΔP = ρgh - h = ΔP / (ρg)

The density of air (ρ) is approximately 1.225 kg/m³, and the acceleration due to gravity (g) is approximately 9.8 m/s².

- h = 2,667.24 Pa / (1.225 kg/m³ * 9.8 m/s²) = 222.68 meters

Therefore, the depth of the mine is approximately 222.68 meters.