Question

Monica wants do protect the environment, but when NASA gives her a "ton of money" to use help build a massive facility on Mars she's all in. During the 6 month voyage there, Monica finds out that air on Mars is pretty much all carbon dioxide and that atmospheric pressure is 0.006 atm at its surface. Given this, how high does Mar's atmosphere go on a warm 5 degrees Celsius Summer day if the air pressure at the very top is 1 Pa? (The surface gravity on Mars is 3.7 m/s^2)

Answer 1

On a warm 5 degrees Celsius Summer day, the height of Mars' atmosphere is approximately 40 kilometers.

Step-by-step explanation:

On a warm 5 degrees Celsius Summer day, the atmospheric pressure on the surface of Mars is 0.006 atm. The air pressure at the very top of Mars' atmosphere is 1 Pa. We can use the information provided to calculate the height of Mars' atmosphere on this day.

To find the height, we can use the relation between pressure, density, and height in an atmosphere. We know that the pressure decreases exponentially with height according to the equation

P = P_0 * exp(-g * h / (R * T)),

where P is the pressure, P_0 is the pressure at the top, g is the acceleration due to gravity, h is the height, R is the gas constant, and T is the temperature.

In this case, we have the pressure at the top as 1 Pa, which is equivalent to 0.00000987 atm. The surface pressure is 0.006 atm. We can have the height of the Mars' atmosphere using the logarithmic difference in pressure.

Using the exponential function with the known values, we can solve for the height:

1. P = P_0 * exp(-g * h / (R * T))
2. 0.006 = 0.00000987 * exp(-3.7 * h / (8.314 * 5 + 273))
3. h = -(log(0.006 / 0.00000987) * (8.314 * 5 + 273)) / (3.7)

Calculating this expression, we get h ≈ 39617 meters or approximately 40 kilometers.

Therefore, on a warm 5 degrees Celsius Summer day, the height of Mars' atmosphere is approximately 40 kilometers.