Question

The temperature and pressure at the surface of Mars during a Martian spring day were determined to be -41 oC 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 oC and the pressure 101.6 kPa (abs).

Answer 1

Answer:

Part a)

$\rho = 0.0205 kg/m^3$

Part b)

$\rho = 1.22 kg/m^3$

So density of atmosphere at Martian Surface is very less than the density at Earth.

Explanation:

Part a)

As per ideal gas equation we know that

$PM = \rho RT$

here we know that Martian atmosphere is equivalent to that of carbon

so we will have

$P = 900 Pa$

$T = 273 - 41 = 232 K$

now we will have

$(900)(0.044) = \rho (8.31)(232)$

$\rho = 0.0205 kg/m^3$

Part b)

Now for the earth surface the density of air is given for

$P = 101.6 kPa$

$T = 18 ^oC$

so we will have

$PM = \rho RT$

$(101.6\times 10^3)(0.029) = \rho(8.31)(273 + 18)$

$\rho = 1.22 kg/m^3$

So density of atmosphere at Martian Surface is very less than the density at Earth.