Question

Approximating Venus's atmosphere as a layer of gas 50 km thick, with uniform density 21 kg/m3, calculate the total mass of the atmosphere.Express your answer using two significant figures.m venus atmosphere = ____ kg

Answer 1

m = 4.9 10⁸ kg

Step-by-step explanation:

The expression for the density is

ρ = m / V

m = ρ V

the volume of the atmosphere is the volume of the sphere of the outer layer of the atmosphere minus the volume of the plant

V = V_atmosphere - V_planet

V = 4/3 π R_atmosphere³ - 4/3 π R_venus³

V = 4/3 π (R_atmosphere³ - R_venus³

)

the radius of the planet is R_venus = 6.06 10⁶ m.

The radius of the outermost layer of the atmosphere

R_atmosphere = 50 10³ + R_ venus = 50 10³ + 6.06 10⁶

R_atmosphere = 6.11 10⁶ m

let's find the volume

V = 4/3 pi [(6,11 10⁶)³ - (6,06 10⁶)³]

V = 23,265 10⁶ m³

let's calculate the mass

m = 21 23,265 10⁶

m = 4.89 10⁸ kg

with two significant figurars is

m = 4.9 10⁸ kg