What is specific heat of the atmosphere?

Question

Total mass of the atmosphere is M = 5e18 kg. Its composiotnion is mostly
nitrogen N2 and oxigen O2 for effective molar mass μ=29 g/mole.

How much energy does it take to increase the temperature of the atmosphere by 1K?
Assume that it has uniform temperature and composition.


Please help me, people...
my dad promised to buy me iPod if I score A on this assignemt.

Answer 1

I'm guessing your dad wouldn't give away the ipod too easily, so I'm going to try and give you as much possibly useful information as i can.

campbelp2002 - according to wikipedia, that's the specific heat capacity of air at sea level (1 atm, 0 degrees celcius). Also, that is the specific heat at constant pressure, whereas I believe we want constant volume, which means we want the Cv of air, at each pressure in the atmosphere.

Here is some information from wikipedia that might help:
Atmospheric pressure is the force per unit area that is applied perpendicularly to a surface by the surrounding gas. The pressure of an atmosphere decreases with altitude due to the diminishing mass of gas above each location. For an atmosphere with a uniform temperature, the scale height is proportional to the temperature and inversely proportional to the mean molecular mass of dry air times the planet's gravitational acceleration. For such a model atmosphere, the pressure declines exponentially with increasing altitude. However, atmospheres are not uniform in temperature, so the exact determination of the atmospheric pressure at any particular altitude is more complex.

He might be looking for some calculus involving integrating pressures based on distance of the air to the center of the earth. I don't know where you can find Cv for different pressures and temperatures, but there must be a way to.

Here is some more information:

http://en.wikipedia.org/wiki/Lapse_rate

Earth's radius = 3960 miles (it's close enough to a sphere)

The average temperature of the atmosphere at the surface of Earth is 14 °C.

Atmospheric pressure decreases with height, dropping by 50% at an altitude of about 5.6 km (equivalently, about 50% of the total atmospheric mass is within the lowest 5.6 km). This pressure drop is approximately exponential, so that each doubling in altitude results in an approximate decrease in pressure by half. However, because of changes in temperature throughout the atmospheric column, as well as the fact that the force of gravity begins to decrease at great altitudes, a single equation does not model atmospheric pressure through all altitudes (it is modeled in 7 exponentially decreasing layers, in the equations given above).
50% of the atmosphere by mass is below an altitude of 5.6 km.
90% of the atmosphere by mass is below an altitude of 16 km.
99.99997% of the atmosphere by mass is below 100 km (almost all of it).
The atmosphere is still persent at heights above 1000 km.

Answer 2

The specific heat of air is variable because the amount of water vapor is variable, but according to wikipedia dry air has a capacity of 1.0035 J per gK, so multiplying your 5e18 kg by 1,000 to convert it to grams and then by 1.012 gives 5.0175e21 Joules of energy. I notice that the table I used gives 20.07 g/mole for dry air, so I may be a little off.

If you score the A, you owe me an iPod.