Question

Высота горы 4000 м. давление у подножия 760 мм рт. ст. Найти давление наверху

Answer 1

800 миллиметров ртутного столба

Answer 2

Calculating Pressure at the Top of the Mountain

To calculate the pressure at the top of the mountain, we can use the relationship between pressure and altitude. The pressure at a certain altitude can be calculated using the formula:

P = P₀ * (1 - (L * h) / T₀) ^ (gM / RL)

Where: - P = pressure at the given altitude - P₀ = pressure at sea level (760 mmHg or 101.3 kPa) - L = temperature lapse rate (approximately 0.0065 K/m) - h = altitude above sea level (4000 m) - T₀ = standard temperature at sea level (approximately 288 K) - g = acceleration due to gravity (approximately 9.81 m/s²) - M = molar mass of Earth's air (approximately 0.029 kg/mol) - R = universal gas constant (approximately 8.314 J/(mol·K)) - L = temperature lapse rate (approximately 0.0065 K/m)

Let's calculate the pressure at the top of the mountain using the given altitude and pressure at the base.

Step 1: Convert the pressure at the base from mmHg to kPa. Step 2: Use the formula to calculate the pressure at the top of the mountain.

Calculations:

Step 1: The pressure at the base is 760 mmHg. Converting this to kPa: 1 mmHg = 0.133322 kPa So, 760 mmHg = 760 * 0.133322 kPa = 101.3 kPa

Step 2: Using the formula: P = 101.3 * (1 - (0.0065 * 4000) / 288) ^ (9.81 * 0.029 / (8.314 * 0.0065))

Result:

The pressure at the top of the mountain is approximately 460 mmHg.