Lapse Rate Definition and Atmospheric Layers

The lapse rate refers to the rate at which atmospheric temperature changes with an increase in altitude.

• Troposphere: Temperature typically decreases with height. This is a positive lapse rate, averaging about 6.5 K/km.
• Stratosphere: Temperature generally increases with height due to ozone absorption of ultraviolet radiation. This is a negative lapse rate (temperature inversion).
• Mesosphere: Temperature decreases with height, similar to the troposphere, exhibiting a positive lapse rate.

Mesosphere Temperature Profile and Lapse Rate Calculation

The question provides the temperature profile for the mesosphere in mid-latitudes:

• At 50 km altitude, the temperature is 270 K.
• At 85 km altitude, the temperature is 180 K.

To calculate the lapse rate in the mesosphere:

1. Calculate the change in altitude:

   $\Delta z = 85 \text{ km} - 50 \text{ km} = 35 \text{ km}$

2. Calculate the change in temperature:

   $\Delta T = 270 \text{ K} - 180 \text{ K} = 90 \text{ K}$

3. Calculate the lapse rate:

   Lapse Rate_Mesosphere $= \frac{\Delta T}{\Delta z} = \frac{90 \text{ K}}{35 \text{ km}} \approx 2.57 \text{ K/km}$

Comparing Mesosphere vs. Troposphere Lapse Rates

We need to compare the calculated mesosphere lapse rate with the typical troposphere lapse rate.

• Lapse Rate_Mesosphere $\approx 2.57 \text{ K/km}$ (temperature decreases with height).
• Lapse Rate_Troposphere $\approx 6.5 \text{ K/km}$ (temperature decreases with height).

Comparing the values:

$2.57 \text{ K/km} < 6.5 \text{ K/km}$

Conclusion: Mesosphere Lapse Rate Smaller

The calculation shows that the lapse rate in the mesosphere (approx. 2.57 K/km) is indeed smaller than the average lapse rate in the troposphere (approx. 6.5 K/km).

Therefore, the statement "Lapse rate in the mesosphere is smaller than that in the troposphere" is correct.