What is the total mass of the Earth’s atmosphere? (The radius of the Earth is
6.37x106m, and atmospheric pressure at the surface is 1.013x105N/m2.)?
To calculate the total mass of the Earth's atmosphere, we can use the formula for pressure in a fluid:
Pressure = Density * Acceleration due to gravity * Height
We know the pressure at the surface of the Earth is 1.013x10^5 N/m^2, the radius of the Earth is 6.37x10^6 m, and the acceleration due to gravity is approximately 9.81 m/s^2.
Using the formula for pressure, we can rearrange it to solve for density:
Density = Pressure / (Acceleration due to gravity * Height)
Plugging in the values, we get:
Density = 1.013x10^5 N/m^2 / (9.81 m/s^2 * 6.37x10^6 m)
Density ≈ 0.00123 kg/m^3
Now, we can calculate the volume of the Earth's atmosphere using the formula for the volume of a sphere:
Volume = 4/3 * π * (Radius)^3
Volume = 4/3 * π * (6.37x10^6 m)^3
Volume ≈ 1.08x10^21 m^3
Finally, we can calculate the total mass of the Earth's atmosphere using the formula:
Mass = Volume * Density
Mass = 1.08x10^21 m^3 * 0.00123 kg/m^3
Mass ≈ 1.33x10^18 kg
Therefore, the total mass of the Earth's atmosphere is approximately 1.33x10^18 kg.