What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 × 10⁶ m, and 1 atm = 1.01 × 10⁵ N/m². A)5.3 × 10¹⁶kg B)1.1 × 10¹⁸ kg C)5.3 × 10¹⁸ kg D)1.1 × 10²⁰ kg E)5.3 × 10⁹ kg

Question

Quizplus · Accepted Answer

To find the total mass of the Earth's atmosphere, we need to use the equation: 
mass = pressure x volume 
We know the pressure (1 atm = 1.01 × 10^5 N/m^2) and the radius of the Earth (6.4 × 10^6 m), but we need to find the volume of the atmosphere.

The atmosphere is approximately 100 km thick, so we can assume that the volume of the atmosphere is equivalent to the volume of a sphere with a radius of 6.5 × 10^6 m (6.4 × 10^6 m + 100 km).

The volume of a sphere is given by the equation: 
volume = (4/3) x pi x radius^3

So, the volume of the atmosphere is: 
volume = (4/3) x pi x (6.5 × 10^6)^3 = 1.09 × 10^21 m^3

Now we can calculate the mass of the atmosphere: 
mass = pressure x volume = (1.01 × 10^5 N/m^2) x (1.09 × 10^21 m^3) = 5.3 × 10^18 kg

Therefore, the answer is C (5.3 × 10^18 kg).

What Is the Total Mass of the Earth's Atmosphere? the Radius