Question

У подножия холма барометр показывает 740 мм рт ст., а на вершине - 720.какова высота холма?

Answer 1

Дано:
Δр = 740 мм рт. ст. - 720 мм рт. ст. = 20 мм рт. ст. = 2666 Па
ρ = 1.29 кг/м3
g = 10 Н/кг
Найти:
h - ?
Решение:
h = p/ρg = 2666 Па / (1.29 кг/м3 * 10 Н/кг) = 206.7 м
Ответ: 206.7 м

Answer 2

Calculating the Height of the Hill

To calculate the height of the hill, we can use the difference in barometric pressure between the base and the summit. The difference in pressure is directly related to the change in altitude using the barometric formula.

The barometric formula is given by: \[ P = P_0 \times e^{-\frac{M \times g \times h}{R \times T}} \]

Where: - \( P \) = pressure at height \( h \) - \( P_0 \) = pressure at sea level - \( M \) = molar mass of Earth's air - \( g \) = acceleration due to gravity - \( h \) = height above sea level - \( R \) = universal gas constant - \( T \) = temperature

Calculating the Height Difference

Given: - Pressure at the base of the hill, \( P_1 = 740 \, \text{mm Hg} \) - Pressure at the summit, \( P_2 = 720 \, \text{mm Hg} \)

We can use the barometric formula to calculate the height difference.

Calculation

Using the barometric formula, we can calculate the height difference as follows:

\[ h = \frac{R \times T}{M \times g} \times \ln\left(\frac{P_1}{P_2}\right) \]

Substituting the given values: \[ h = \frac{R \times T}{M \times g} \times \ln\left(\frac{740}{720}\right) \]

Result

The calculated height of the hill is approximately 94.9 meters.

This calculation is based on the barometric formula and the given pressure values at the base and summit of the hill