How to Calculate Temperature & Height Using Lapse
Rates
By Erik Thomsen, eHow Contributor
Typically, temperature decreases as
height increases.
Height, temperature and lapse rate
are all related. If you have any two of these numbers, you will be able to
figure out the third. The most common lapse rate used is referred to as the
environmental lapse rate (ELR). According to Yochanan Kushnir of Colombia
College, the relationship between these three variables can be expressed as:
ELR = - (dTemperature / dHeight)
To calculate temperature or height using the ELR, plug the information you know into the equation, and solve for the unknown variable.
ELR = - (dTemperature / dHeight)
To calculate temperature or height using the ELR, plug the information you know into the equation, and solve for the unknown variable.
Instructions
1.
Calculating
Temperature Using Height and ELR
a)
You will need to set up your
equation by plugging in the numbers you already have. If you know the ELR and
the height, you will be able to plug those numbers into your equation and solve
for the temperature. If your ELR is .00378 degrees F/ft and your height is
2,200 feet, you can plug those numbers in to get:
.00378 = -
(dTemperature / 2200)
b)
Get your unknown variable alone on
one side of the equation by multiplying each side by 2200:
(2200)(.00378)
= - ((dTemperature / 2200)(2200))
c)
Simplify your equation using your
calculator:
8.316 = -
dTemperature
Your
change in temperature was - 8.316 degrees F.
2.
Calculating
Height Using Temperature and ELR
d)
If you know the ELR and the
temperature, you will be able to plug those numbers into your equation and
solve for the height. If your ELR is .00299 degrees F/ft and your temperature
is 16.67 degrees F, you can plug those numbers in to get:
.00299 =
16.67 / dHeight
e)
Solve for dHeight by dividing each
side of the equation by .00299:
(.00299 /
.00299) = - ((16.67 / dHeight) / .00299)
f)
Simplify your equation using your
calculator:
1 = -
(.049843 / dHeight)
g)
Multiply each side of the equation
by dHeight:
(1)(dHeight)
= - ((.049843 / dHeight)(dHeight))
h)
Simplify your equation to find
dHeight:
dHeight =
- .049843 ft
