Question

The temperature of the atmosphere is not always constant and can increase or decrease with height. In a neutral atmosphere, where there is not a significant amount of vertical mixing, the temperature decreases at a rate of approximately 6.5 K per km. The magnitude of the decrease in temperature as height increases is known as the lapse rate (=6.5K/km−Γ=6.5K/km). Assume that the surface pressure is p 0=1.013×10⁵ Pa where293T=293K and the lapse rate is (−Γ=6.5K/km). Estimate the pressure 3.0 km above the surface of Earth.

a. p=8.32×10⁴Pa

b. p=9.75×10⁴ Pa

c. p=1.05×10⁵ Pa

d. p=1.20×10⁵Pa

Answer 1

To estimate the pressure 3.0 km above the surface of Earth, we can use the lapse rate and the given surface pressure. The temperature and pressure in the atmosphere are related, so we can assume the pressure decreases at the same rate as the temperature. Plugging in the values, the estimated pressure is approximately 8.32 × 10^4 Pa.

Step-by-step explanation:

To estimate the pressure 3.0 km above the surface of Earth, we can use the lapse rate and the given surface pressure. The lapse rate tells us that the temperature decreases at a rate of 6.5 K per km. Since the temperature and pressure are related in the atmosphere, we can assume that the pressure decreases at the same rate.

So, at 3.0 km above the surface, the decrease in pressure would be 3.0 km multiplied by the lapse rate (-Γ = 6.5 K/km). We can then calculate the pressure at that height by subtracting the decrease from the surface pressure:

p = p0 - (3.0 km * 6.5 K/km)

Plugging in the values, we get:

p = 1.013 × 10^5 Pa - (3.0 km * 6.5 K/km)

Simplifying the equation, we find that p is approximately 8.32 × 10^4 Pa.