At 2 km above the atmosphere, the temperature for a parcel of dry air is 10 ooC and pressure is 800 hPa. What is the potential temperature of this air parcel? Cpp of air 1.005 kJ/kgK and ideal gas constant of air is 0.287 kJ/kgK 290 K 296 K 302 K 308 k

The potential temperature is the temperature that a parcel of air would have if it were brought adiabatically (i.e., without exchange of heat or mass) to a standard reference pressure, typically 1000 hPa (hectopascals). The formula to calculate the potential temperature (θ) is:

θ = T * (1000/P)^(R/Cp)

where:

• T is the actual temperature in Kelvin
• P is the actual pressure in hPa
• R is the ideal gas constant for air (0.287 kJ/kgK)
• Cp is the specific heat capacity of air at constant pressure (1.005 kJ/kgK)

First, convert the given temperature from Celsius to Kelvin. The conversion formula is T(K) = T(C) + 273.15. So, T = 10°C + 273.15 = 283.15 K.

Then, substitute the known values into the potential temperature formula:

θ = 283.15 * (1000/800)^(0.287/1.005)

Solving the equation gives the potential temperature θ ≈ 290 K. So, the potential temperature of the air parcel is approximately 290 K.