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 × 10¹⁶ kg B) 1.1 × 10¹⁸ kg C) 5.3 × 10¹⁸ kg D) 1.1 × 10²⁰ kg E) 5.3 × 10⁹ kg

Question

Quizplus · Accepted Answer

The total mass of the Earth's atmosphere can be calculated using the formula:

Mass = Pressure x Volume / (Ideal Gas Constant x Temperature)

First, we need to calculate the total volume of the Earth's atmosphere. We know that the Earth's radius is 6.4 x 10^6 m, so the total volume of the atmosphere can be calculated as:

Volume = (4/3) x π x (6.4 x 10^6)^3 = 1.086 x 10^21 m^3

Next, we can calculate the total pressure of the atmosphere using the given information that 1 ATM = 1.01 x 10^5 N/m^2:

Pressure = 1 ATM = 1.01 x 10^5 N/m^2

Finally, we need to assume a temperature and gas constant. The temperature of the atmosphere varies widely depending on altitude and other factors, but we can assume an average temperature of around 15°C or 288 K. The gas constant for air is 287 J/(kg·K). Using these values, we can calculate the total mass of the Earth's atmosphere:

Mass = (1.01 x 10^5 N/m^2) x (1.086 x 10^21 m^3) / (287 J/(kg·K) x 288 K)

Mass = 5.3 x 10^18 kg

Therefore, the best choice is C, 5.3 × 10^18 kg.

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