Question

Зафіксувавши показники атмосферного тиску біля підніжжя гори (540 мм рт. ст.), група альпіністів піднялася на її вершину, де барометр показав 225 мм рт. ст. Яка висота гори?

Answer 1

Ответ:

Пам'ятаємо, що при кожному піднятті вгору на 1000 м, тиск знижується на 100 мм. рт. ст,

Робимо пропорцію:

540-225=315 мм рт. ст.

100 мм. рт. ст.-1000 м

315 мм рт.ст.- х

х= 315×1000/100= 3150 м- висота гори

Answer 2

Calculation of Mountain Height based on Barometric Pressure

To calculate the height of the mountain based on the difference in barometric pressure, we can use the barometric formula, which relates the change in pressure to the change in altitude. The formula is as follows:

P2 = P1 * (1 - (L * h2) / T)

Where: - P1 is the initial pressure at the base of the mountain - P2 is the pressure at the summit of the mountain - L is the temperature lapse rate (change in temperature with altitude) - h2 is the height of the mountain - T is the temperature at the base of the mountain

In this case, we are given the initial pressure at the base of the mountain (540 mmHg) and the pressure at the summit of the mountain (225 mmHg). We need to find the height of the mountain (h2).

Finding the Temperature Lapse Rate

To solve the equation, we need to know the temperature lapse rate (L). The temperature lapse rate is the rate at which the temperature decreases with increasing altitude. It is typically around 6.5 degrees Celsius per kilometer (6.5 °C/km) in the troposphere.

However, since we do not have the temperature lapse rate for this specific mountain, we will assume a standard temperature lapse rate of 6.5 °C/km for our calculation.

Calculation

Let's assume the temperature at the base of the mountain is 15 °C. We can now substitute the given values into the barometric formula and solve for the height of the mountain (h2).

225 mmHg = 540 mmHg * (1 - (6.5 °C/km * h2) / 15 °C)

Simplifying the equation:

225 / 540 = 1 - (6.5/15) * h2

0.4167 = 1 - 0.4333 * h2

0.4333 * h2 = 1 - 0.4167

0.4333 * h2 = 0.5833

h2 = 0.5833 / 0.4333

h2 ≈ 1.347 km

Therefore, the approximate height of the mountain is 1.347 kilometers.

Please note that this calculation assumes a standard temperature lapse rate and may not be entirely accurate. Additionally, other factors such as local weather conditions and variations in temperature lapse rate can affect the accuracy of this calculation.