Question

Барометр подняли со дна шахты. Показание барометра изменились с 770 мм.рт.ст. на 745 мм.рт.ст. Температура окружающей среды 0 градусов. Какова высота шахты?

Answer 1

При небольших изменениях высоты при изменении давления на 1 мм рт ст высота меняется на 12 метров
1 Найдем разность давлений   P1-P2=770-745=25 мм рт ст
Найдем глубину шахты
h= 12м*25= 300 м

Answer 2

Calculation of the Height of the Shaft

To calculate the height of the shaft, we can use the relationship between atmospheric pressure and altitude. As we know the change in barometric pressure and the temperature of the surrounding environment, we can apply the barometric formula to determine the height.

The barometric formula states that the pressure at a given altitude is related to the pressure at sea level by the equation:

P = P0 * (1 - (L * h) / T0)^(g / (R * L))

Where: - P is the pressure at the given altitude - P0 is the pressure at sea level - L is the temperature lapse rate (change in temperature with altitude) - h is the height above sea level - T0 is the temperature at sea level - g is the acceleration due to gravity - R is the gas constant

In this case, we have the following information: - P0 = 770 mmHg (pressure at sea level) - P = 745 mmHg (pressure at the given altitude) - T0 = 0 degrees Celsius (temperature at sea level) - L is not provided in the question, so we will assume a standard lapse rate of 6.5 degrees Celsius per kilometer - g is approximately 9.8 m/s^2 - R is approximately 8.314 J/(mol·K)

Let's calculate the height of the shaft using the barometric formula:

745 = 770 * (1 - (6.5 * h) / 273.15)^(9.8 / (8.314 * 6.5))

Simplifying the equation, we get:

(1 - (6.5 * h) / 273.15)^(0.001196) = 0.9662

Taking the natural logarithm of both sides, we have:

ln(1 - (6.5 * h) / 273.15)^(0.001196) = ln(0.9662)

Simplifying further, we get:

(6.5 * h) / 273.15 = -0.0342

Solving for h, we find:

h = (-0.0342 * 273.15) / 6.5

Calculating this expression, we find that the height of the shaft is approximately -1.44 meters.

Please note that the negative sign indicates that the shaft is below sea level. However, it is important to verify the accuracy of this calculation, as the provided sources do not contain relevant information to confirm the calculation.