What is the thickness of the layer from 1000 - 850 mb if the mean temperature of the layer is 2 C?
From what it says in my textbook it seems as if mb = hPa so all you do is 850 - 1000 = -150 hPa but I am pretty sure that is wrong because what do you do with the temperature??
THANKS!
To determine the thickness of a layer between two pressure levels, the temperature difference within that layer needs to be taken into account. The thickness is directly related to the mean temperature of the layer.
To calculate the thickness, you can use the hypsometric equation, which relates the thickness (Z) of a layer to the mean temperature (T) of that layer and the difference in pressure level (ΔP):
Z = (Rd * T * ΔP) / (g * P)
Where:
- Z = thickness of the layer
- Rd = gas constant for dry air (~287 J/(kg*K))
- T = mean temperature of the layer in Kelvin (K)
- ΔP = pressure difference between the two levels (in pascals - Pa)
- g = acceleration due to gravity (~9.8 m/s^2)
- P = average of the pressures at the two levels (in pascals - Pa)
Given that the mean temperature of the layer is 2°C, we need to convert it to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature. Therefore, 2°C + 273.15 = 275.15 K.
Next, we need to convert the pressure levels from millibars (mb) to pascals (Pa). Since 1 hPa = 1 millibar, we can use the same values for ΔP and P.
Now we can substitute the values into the equation:
ΔP = 850 hPa - 1000 hPa = -150 hPa = -150 * 100 = -15000 Pa
P = (850 hPa + 1000 hPa) / 2 = 925 hPa = 925 * 100 = 92500 Pa
T = 275.15 K
Plugging these values into the equation, we get:
Z = (287 * 275.15 * -15000) / (9.8 * 92500)
Simplifying the equation gives us:
Z ≈ - 1042.29 meters
Therefore, the thickness of the layer between the 1000 and 850-millibar levels, with a mean temperature of 2°C, is approximately -1042.29 meters. Note that the negative sign indicates a decrease in height or a descent within the layer.