Physics 2016 JAMB Past Questions - Question 19: The height at which the atmosphere ceases to exist is about 80 km. If the atmosphere pressure on the ground level is 760mmHg,the pressure at a height of 20km above the ground level is

Correct Answer

A

Explanation

P = P₀ * exp(-M * g * h / (R * T))

Where:
P is the pressure at the given altitude,
P₀ is the pressure at the ground level (760 mmHg in this case),
M is the molar mass of Earth's air (approximately 0.029 kg/mol),
g is the acceleration due to gravity (approximately 9.8 m/s²),
h is the height above the ground level (20 km = 20,000 m),
R is the ideal gas constant (approximately 8.314 J/(mol·K)),
T is the temperature in Kelvin.

Since the temperature is not given, we'll assume a standard temperature profile where the temperature decreases at a rate of 6.5°C per kilometer until the tropopause, which is approximately 11 km above the ground level. Above the tropopause, the temperature remains constant.

To convert the pressure from mmHg to Pascal, we'll use the conversion factor: 1 mmHg = 133.322 Pascal.

Let's calculate the pressure at a height of 20 km above the ground level:

First, we need to convert the pressure at the ground level from mmHg to Pascal:
P₀ = 760 mmHg * 133.322 Pascal/mmHg ≈ 101,325 Pascal

Next, we need to calculate the temperature at the given altitude:
T = T₀ - L * h
T₀ = 288.15 K (standard temperature at sea level)
L = 6.5°C/km = 6.5 K/km (temperature lapse rate)

T = 288.15 K - 6.5 K/km * 20 km ≈ 155.65 K

Now, we can calculate the pressure at a height of 20 km using the barometric formula:
P = 101,325 * exp(-0.029 * 9.8 * 20,000 / (8.314 * 155.65))

Calculating this expression gives us:
P ≈ 54,526 Pascal

Therefore, the pressure at a height of 20 km above the ground level is approximately 54,526 Pascal.