Question

Відносна вологість повітря при температурі 15°С дорівнює 70%. Якою стане відносна вологість, якщо температуру підвищити до 30°С, а об'єм повітря зменшити в 2 рази?​

Answer 1

Відповідь:

За законом Бойля-Маріотта об'єм і температура взаємодіють із зміною тиску, тому можна скористатися формулою:

p1 * V1 / T1 = p2 * V2 / T2

де p1 і T1 - тиск і температура вихідного повітря, V1 - його об'єм, p2 і T2 - тиск і температура нового повітря, V2 - його об'єм.

Вихідне повітря має тиск, який дорівнює нормальному атмосферному тиску 760 мм рт. ст., а температуру 15 °С, тому можна записати:

760 * V1 / 288 = p2 * V2 / 303

Після зменшення об'єму повітря в 2 рази V2 = V1 / 2, тому можна переписати формулу:

760 * V1 / 288 = p2 * V1 / 2 / 303

Розв'язавши рівняння відносно p2, отримаємо:

p2 = 760 * 303 / 144 = 1596.25 мм рт. ст.

Тепер можна знайти відносну вологість при новій температурі:

70% * (273 + 15) / (273 + 30) * 1596.25 / 760 = 73.4%

Отже, відносна вологість збільшиться з 70% до 73.4%, якщо підвищити температуру до 30°С і зменшити об'єм повітря в 2 рази.

Answer 2

Relative Humidity Calculation

To calculate the new relative humidity when the temperature is increased to 30°C and the volume of air is reduced by 2 times, we need to consider the relationship between temperature, volume, and relative humidity.

The relative humidity is a measure of the amount of moisture present in the air compared to the maximum amount of moisture the air can hold at a given temperature. It is expressed as a percentage.

To calculate the new relative humidity, we can use the concept of the "dew point temperature." The dew point temperature is the temperature at which the air becomes saturated and condensation begins to form. At this temperature, the air is holding as much moisture as it can.

To find the new relative humidity, we need to compare the dew point temperature at 15°C with the dew point temperature at 30°C. Since the volume of air is reduced by 2 times, we can assume that the amount of moisture in the air remains constant.

Calculation Steps:

1. Find the dew point temperature at 15°C using the given relative humidity of 70%. We can assume that the air is saturated at this temperature. 2. Find the dew point temperature at 30°C by using the same amount of moisture in the air. 3. Calculate the new relative humidity at 30°C by comparing the dew point temperature at 30°C with the actual temperature.

Step 1: Finding the Dew Point Temperature at 15°C

Since the air is saturated at 15°C, the dew point temperature is equal to the actual temperature. Therefore, the dew point temperature at 15°C is 15°C.

Step 2: Finding the Dew Point Temperature at 30°C

To find the dew point temperature at 30°C, we need to use the same amount of moisture in the air. Since the volume of air is reduced by 2 times, the concentration of moisture in the air will also be reduced by 2 times.

Therefore, the new dew point temperature at 30°C can be calculated by dividing the original dew point temperature at 15°C by 2.

New dew point temperature at 30°C = 15°C / 2 = 7.5°C

Step 3: Calculating the New Relative Humidity at 30°C

To calculate the new relative humidity at 30°C, we compare the dew point temperature at 30°C (7.5°C) with the actual temperature (30°C).

We can use a psychrometric chart or an online calculator to find the new relative humidity. However, since we don't have access to a specific chart or calculator, we can estimate the new relative humidity based on the difference between the actual temperature and the dew point temperature.

The larger the difference between the actual temperature and the dew point temperature, the lower the relative humidity. Conversely, the smaller the difference, the higher the relative humidity.

In this case, the difference between the actual temperature (30°C) and the dew point temperature (7.5°C) is 22.5°C.

Based on this difference, we can estimate that the new relative humidity at 30°C will be lower than 70%.

Please note that this is an estimation, and the actual value may vary depending on various factors.

Conclusion

To summarize, the new relative humidity at 30°C, with the volume of air reduced by 2 times, will be lower than 70%. The exact value cannot be determined without more specific information or access to a psychrometric chart or calculator.