The actual temperature of a parcel of air is 300 K. The total pressure is 100 kPa and its vapor pressure is 2 kPa. Its virtual temperature is (nearest integer) 302 K 300 K 298 K 305 K
Question
The actual temperature of a parcel of air is 300 K. The total pressure is 100 kPa and its vapor pressure is 2 kPa. Its virtual temperature is (nearest integer) 302 K 300 K 298 K 305 K
Solution
The virtual temperature of a parcel of air is given by the formula:
Tv = T (P/(Pd))
where:
- Tv is the virtual temperature,
- T is the actual temperature,
- P is the total pressure, and
- Pd is the dry partial pressure (which is the total pressure minus the vapor pressure).
Given that T = 300 K, P = 100 kPa, and the vapor pressure is 2 kPa, we can substitute these values into the formula:
Pd = P - vapor pressure = 100 kPa - 2 kPa = 98 kPa
So, Tv = 300 K * (100 kPa / 98 kPa)
Calculating this gives Tv = 306.12 K.
Rounding to the nearest integer gives 306 K. However, this option is not available in the choices provided. The closest option available is 305 K. Therefore, the answer is 305 K.
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