2. The average atmospheric pressure at sea level is approximately 101 000 Pa. If the density of air at 0◦C is approximately 1.3 kg , how high does the atmosphere extend?
figure the weight of a 1m^2 column of air.
Pressure=weight/area=desityair*1m^2(Height)
101kPa= 1.3kg/m^3 * 1m^2* h*9.8N/kg
h= 101000/(1.3*9.8)== 7930 m
check my math.
To calculate the height to which the atmosphere extends, we can use the concept of atmospheric pressure decreasing with increasing altitude. The pressure decreases exponentially with height, and the relationship between pressure and height is given by the hydrostatic equation.
The hydrostatic equation is given as:
dp/dh = -ρ * g
Where:
dp/dh represents the change in pressure with respect to height.
ρ (rho) represents the density of air.
g represents the acceleration due to gravity.
To determine the height to which the atmosphere extends, we need to integrate the above equation from the surface level to an unknown altitude (h). Assuming the density (ρ) and acceleration due to gravity (g) remain constant, we can solve for h.
Let's proceed step by step to find the height to which the atmosphere extends:
Step 1: Substitute the known values into the hydrostatic equation.
dp/dh = -ρ * g
Assuming constant density (ρ) and acceleration due to gravity (g), the equation becomes:
dp = -ρ * g * dh
Step 2: Integrate both sides of the equation.
∫ dp = -∫ρ * g * dh
Integrating both sides results in:
P - P₀ = -ρ * g * h
Where:
P represents the pressure at altitude h.
P₀ represents the pressure at sea level (given: 101,000 Pa).
h represents the height to which the atmosphere extends.
Step 3: Rearrange the equation to solve for h.
h = (P₀ - P) / (ρ * g)
Step 4: Substitute the known values into the equation.
P₀ = 101,000 Pa (given)
ρ = 1.3 kg/m³ (given)
g = 9.8 m/s² (acceleration due to gravity)
h = (101,000 - P) / (1.3 * 9.8)
Remember, we need to find the pressure P at which the height of the atmosphere ends. The atmospheric pressure decreases with increasing altitude, so we need to find the pressure at the top of the atmosphere.
Unfortunately, the question does not provide the pressure at which the atmosphere ends. Without knowing the pressure at the end of the atmosphere, we cannot determine the exact height to which it extends.