Question

The temperature and pressure at the surface of Mars during a Martian spring day were determined to be -50 °C and 900 Pa, respectively. (a)Determine the density of the Martian atmosphere for these conditions if the gas constant for the Martian atmosphere is assumed to be equivalent to that of carbon dioxide. (b) Compare the answer from part (a) with the density of the Earth’s atmosphere during a spring day when the temperature is 18 °C and the pressure 101.6 kPa

Answer 1

Answer:

(a) The density of the Martian atmosphere is 0.021kg/m^3

(b) The density of the Martian atmosphere (0.021kg/m^3) is less than the density of the Earth's atmosphere (1.217kg/m^3)

Explanation:

(a) Density of Martian atmosphere (D) = P/RT

P = 900 Pa, R = 189 J/kgK, T = -50°C = -50+273 = 223K

D = 900/189×223 = 900/42,147 = 0.021kg/m^3

b) Density of Earth's atmosphere (D) = P/RT

P = 101.6kPa = 101.6×1000 = 101,600 Pa, R = 287 J/kgK, T = 18°C = 18+273 = 291K

D = 101,600/287×291 = 101,600/83,517 = 1.217kg/m^3

The density of Martian atmosphere is less than the density of the Earth's atmosphere

Answer 2

Answer:

T = 273 + (-50) = 273 – 50 = 223 K

R = 188.82 J / kg K for CO2

Density (Martian Atmosphere) = P / RT = 900 / 188.92 x 223 = 900 / 42129.16 = 0.0213 kg / $m^{3}$

T = 273 +18 = 291 K, R = 287 J / kg k (for air) P = 101.6 k Pa = 101600 Pa

Density (Earth Atmosphere) = P / RT = 101600 / 287 x 291 = 1.216 kg / $m^{3}$