Question

In the troposphere, as altitude increases, air temperature drops at a relatively uniform rate. At the top of the troposphere, an average height of 11 km, the average temperature is −56.5°C. At the base of the troposphere, 0 km, the average temperature is 15°C.

In a linear model of this situation, which of the following statements applies?
A.
An increase of 1 km in altitude corresponds to a increase of 6.5°C in temperature.
B.
An increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.
C.
An increase of 1 km in altitude corresponds to a increase of 3.8°C in temperature.
D.
An increase of 1 km in altitude corresponds to a decrease of 3.8°C in temperature.

Answer 1

To find the correct answer, we need to determine the rate of temperature change with respect to altitude in the troposphere.

We know:
- At 0 km (the base of the troposphere), the temperature is 15°C.
- At 11 km (the top of the troposphere), the temperature is −56.5°C.

First, we calculate the total change in temperature:

Change in temperature = Final temperature - Initial temperature = -56.5°C - 15°C = -71.5°C.

Next, we determine the change in altitude:

Change in altitude = Final altitude - Initial altitude = 11 km - 0 km = 11 km.

Now, we can find the rate of temperature change per kilometer of altitude:

Rate of temperature change = Change in temperature / Change in altitude
= -71.5°C / 11 km
≈ -6.5°C/km.

This indicates that for every 1 km increase in altitude, the temperature decreases by about 6.5°C.

Therefore, the correct statement is:

**B. An increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.**