Question

Определите относительную влажность воздуха, если при температуре +30 в нем содержится 3г водяного пара

Answer 1

При температуре +30 в воздухе может содержатся около 30 г водяного пара. Теперь разделим 3 на 30 и переведем в проценты - итого 10%.

Answer 2

Relative Humidity Calculation

To determine the relative humidity, we can use the formula:

Relative Humidity = (Actual Water Vapor Pressure / Saturation Water Vapor Pressure) × 100%

First, we need to calculate the saturation water vapor pressure at the given temperature of 30°C. Then, we can use the given water vapor content to find the actual water vapor pressure.

Saturation Water Vapor Pressure at 30°C

The saturation water vapor pressure at 30°C can be calculated using the Antoine equation:

ln(P) = A - (B / (C + T))

Where: - P is the saturation vapor pressure in mmHg - T is the temperature in degrees Celsius - A, B, and C are constants specific to water

Using the Antoine equation, we can calculate the saturation water vapor pressure at 30°C.

Calculation

Using the Antoine equation for water vapor at 30°C: ln(P) = 7.96681 - (1668.21 / (228.0 + 30))

Calculating the value of P: P ≈ 31.824 mmHg

Actual Water Vapor Pressure

Given that the air contains 3g of water vapor at 30°C, we can convert this to mmHg using the ideal gas law and the molecular weight of water.

Calculation

Using the ideal gas law: PV = nRT

Where: - P is the pressure in mmHg - V is the volume in liters - n is the number of moles - R is the ideal gas constant - T is the temperature in Kelvin

Converting 3g of water to moles: n = (3g) / (18.01528g/mol) ≈ 0.1666 moles

Using the ideal gas constant: R = 0.0821 L atm / K mol

Converting temperature to Kelvin: 30°C + 273.15 ≈ 303.15 K

Using the ideal gas law to find the pressure: P = (0.1666 moles) * (0.0821 L atm / K mol) * (303.15 K) / (1 L) ≈ 4.28 atm ≈ 325.5 mmHg

So, the actual water vapor pressure is approximately 325.5 mmHg.

Relative Humidity Calculation

Now, we can calculate the relative humidity using the formula:

Relative Humidity = (Actual Water Vapor Pressure / Saturation Water Vapor Pressure) × 100%

Substituting the values: Relative Humidity ≈ (325.5 mmHg / 31.824 mmHg) × 100% ≈ 1023%

Therefore, the relative humidity at 30°C with 3g of water vapor in the air is approximately 1023%.