Carbon Dioxide in the Martian Ice Caps

[Raptor112]

Homework Statement

The Viking landers on Mars measured a seasonal change in surface pressure of 2.5 mb due
to the variation in the seasonal extent of the ice caps. Ignoring any elevation variations on
the surface of Mars, calculate the difference in the total mass of CO2 in both ice caps
between the maximum and minimum in surface pressure.

Radius of Mars =3390km
Mass of Mars = 6.42 × 1023 kg
Universal gravitation constant G = 6.67 × 10-11 N m^2 kg-2

 

[Bystander]

Step at a time: Step one?

 

[Matt Scherma]

This implicitly makes no sense to me: if PV=nrT, and n increases, then sure P will increase but what is V? Surely they don't expect you to calculate some rbritrary volume from the radius of Mars to 2 meters above that? Very confusing.
If anyone else can actually help it would really be appreciated.

 

[SteamKing]

This implicitly makes no sense to me: if PV=nrT, and n increases, then sure P will increase but what is V? Surely they don't expect you to calculate some rbritrary volume from the radius of Mars to 2 meters above that? Very confusing.
If anyone else can actually help it would really be appreciated.

Who says that PV = nRT applies here?

When the 'ice' caps on Mars sublime and release extra CO₂ into the atmosphere, there is a small increase in the surface pressure. What does this increase in pressure tell you about the mass of the atmosphere?

On earth, standard atmospheric pressure is 101,325 Pa. What is the relationship between atmospheric pressure and the mass of the atmosphere on earth?

 

[Matt Scherma]

Who says that PV = nRT applies here?

When the 'ice' caps on Mars sublime and release extra CO₂ into the atmosphere, there is a small increase in the surface pressure. What does this increase in pressure tell you about the mass of the atmosphere?

On earth, standard atmospheric pressure is 101,325 Pa. What is the relationship between atmospheric pressure and the mass of the atmosphere on earth?

This actually makes sense thanks, PV=nRT was my first port of call when dealing with systems of pressure, volume and quantity of gas.
Per unit volume, for example a cylinder of flat surface area A, the pressure pushing down from above is mg, where m is the amount of gas contained in a cylinder of equal radius extending to the top of the atmosphere.

I found another equation online:
M_A=4*Pi*R^2/g
do you think this applies to the situation correctly? If so we can just use this to create a Delta M_A if we can calculate g and know M

 

[SteamKing]

This actually makes sense thanks, PV=nRT was my first port of call when dealing with systems of pressure, volume and quantity of gas.
Per unit volume, for example a cylinder of flat surface area A, the pressure pushing down from above is mg, where m is the amount of gas contained in a cylinder of equal radius extending to the top of the atmosphere.

I found another equation online:
M_A=4*Pi*R^2/g
do you think this applies to the situation correctly? If so we can just use this to create a Delta M_A if we can calculate g and know M

The physical properties of Mars (diameter, surface gravity, atmospheric pressure) can be looked up.

The equation for M_A above seems to be missing a key component for the calculation of the mass of the atmosphere. Can you spot it?

 

[Matt Scherma]

The physical properties of Mars (diameter, surface gravity, atmospheric pressure) can be looked up.

The equation for M_A above seems to be missing a key component for the calculation of the mass of the atmosphere. Can you spot it?

Oh yes of course, thanks again. Misquoted and missed the pressure there.
I would imagine the equation could then be changed for the purposes of this question to:

DeltaM_A=4*Pi*R^2*DeltaP/g

Then you just have to be careful about the use of units and the question is mathematically simple.

 

[SteamKing]

Oh yes of course, thanks again. Misquoted and missed the pressure there.
I would imagine the equation could then be changed for the purposes of this question to:

DeltaM_A=4*Pi*R^2*DeltaP/g

Then you just have to be careful about the use of units and the question is mathematically simple.

Looks good.