Calculating temperature given altitude

In summary, to calculate the temperature at any given altitude in the troposphere, we can use the ideal gas law and the barometric equation. The ideal gas law states that P1/P2 = V1/V2 * T1/T2, where P is air pressure, V is volume of air, and T is temperature. The barometric equation, which takes into account the decrease in pressure with altitude, is p= p0 exp (–h/A). In the temperate zone, the temperature is expected to decrease at a constant rate of 0.0065 °C/m up to 11 km altitude according to the ICAO Standard atmosphere.
  • #1
moonman239
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Homework Statement


I am trying to figure out how to calculate the temperature at any given altitude in the troposphere.

Homework Equations


Let P=air pressure, V=volume of air above a given altitude, n=number of moles of gas, R=the ideal gas constant, T=temperature, and h=height above sea levelX1 and X2 = the value of X at geographic point 1 and point 2.

PV=nRT (the ideal gas law)
Volume of a sphere = 4/3*pi*radius3
Surface area of a sphere = 4*pi*radius2

The Attempt at a Solution


P1/ P2 = V1nRT1 / V2nRT2.

Now, we don't need to know what n and R are, because they are canceled out of the equation. So ignore them. We are now left with P1/P2 = V1/V2 * T1/T2.

V = 4/3*pi*radius of troposphere - (4/3 * pi * (6371.5+h))
V1 / V2 is pretty obvious and can't be simplified.
 
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  • #2
The main problem that I see with this is that fall off in pressure is governed more by the barometric equation p= p0 exp (–h/A) where A is roughly 7 km, than by an increase in available volume at greater height.

I do not know how meteorologists do this calculation, but the recommendation of the ICAO Standard atmosphere is that the temperature will fall at a constant rate of 0.0065 °C/m up to 11 km altitude in the temperate zone. Obviously that is an "other things being equal" calculation that cannot take account of local atmospheric conditions.
 

1. How does altitude affect temperature?

As altitude increases, the temperature decreases. This is because the air becomes less dense at higher altitudes, making it harder for the air molecules to retain heat.

2. What is the formula for calculating temperature given altitude?

The formula for calculating temperature given altitude is the standard atmospheric lapse rate formula, which is: T = T0 - (L * h), where T is the temperature at altitude h, T0 is the temperature at sea level, and L is the lapse rate.

3. How accurate is the calculation of temperature given altitude?

The calculation of temperature given altitude is relatively accurate, but it is based on a standard atmospheric model and may not account for local weather patterns or other variables. It is best used as an estimate rather than an exact measurement.

4. Can temperature change with altitude even in the same location?

Yes, temperature can change with altitude even in the same location. This is because local weather patterns, such as wind and cloud cover, can affect the temperature at different altitudes. Additionally, temperatures can vary depending on the time of day and season.

5. How does the calculation of temperature given altitude differ in different regions of the world?

The calculation of temperature given altitude may differ in different regions of the world due to variations in the standard atmospheric lapse rate. Additionally, local weather patterns and geographic features can also impact the temperature at different altitudes. It is important to use a reliable source or consult with local experts for accurate calculations in specific regions.

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