Assuming that the air temperature drops 6.5 Celsius degrees per 1000 m, compute the temperature at the tropopause if the sea-level air temperature is 15 C and the altitude of the tropopause is 11 km.

(round to the nearest tenth)

11 * 6.5 = 71.5

15 - 71.5 = -56.5

To compute the temperature at the tropopause, we can use the temperature lapse rate formula:

Temperature change = Lapse rate * Altitude Change

Given:
Sea-level temperature (T1) = 15°C
Altitude at tropopause (H2) = 11 km
Lapse rate (L) = -6.5°C per 1000 m

First, we need to calculate the altitude change (ΔH) between sea level and the tropopause:

ΔH = H2 - H1

Since the tropopause is at an altitude of 11 km and we are considering sea level, where the altitude is 0 m, we have:

ΔH = 11 km - 0 km
ΔH = 11 km

Next, we can calculate the temperature change (ΔT) using the formula:

ΔT = L * ΔH / 1000

Substituting the values we have:

ΔT = -6.5°C per 1000 m * 11 km / 1000
ΔT = -0.0715°C per m * 11000 m
ΔT = -7.865°C

To find the temperature at the tropopause (T2), we need to add or subtract the temperature change from the initial sea-level temperature:

T2 = T1 + ΔT
T2 = 15°C + (-7.865°C)
T2 = 7.135°C

Hence, the temperature at the tropopause is approximately 7.1°C when rounded to the nearest tenth.

To compute the temperature at the tropopause, we can use the lapse rate equation. The lapse rate describes the decrease in temperature with increasing altitude.

Given:
Sea-level air temperature (T1) = 15°C
Lapse rate (LR) = 6.5°C per 1000 m
Altitude of the tropopause (H2) = 11 km

We need to find the temperature at the troposphere (T2).

To calculate T2, we can use the following steps:

1. Convert the altitude of the tropopause to meters:
H2 = 11 km × 1000 m/km = 11000 m

2. Calculate the altitude difference between the sea level and the tropopause:
ΔH = H2 - H1

where H1 is the altitude at sea level, which is 0 m.

ΔH = 11000 m - 0 m = 11000 m

3. Calculate the temperature difference between the sea level and the tropopause:
ΔT = LR × (ΔH / 1000)

where ΔH is the altitude difference in kilometers (converted to meters) and 1000 converts it to kilometers.

ΔT = 6.5°C per 1000 m × (11000 m / 1000) = 6.5°C per 1000 m × 11 = 71.5°C

4. Calculate the temperature at the tropopause:
T2 = T1 - ΔT

where T1 is the sea-level air temperature.

T2 = 15°C - 71.5°C = -56.5°C

Therefore, the temperature at the tropopause is approximately -56.5°C.