Consider equal VOLUMES of water and air (air is mostly nitrogen). If both were to increase in temperature by 3 degrees C, would both gain the same amount of energy?

Question

Consider equal VOLUMES of water and air (air is mostly nitrogen). If both were to increase in temperature by 3 degrees C, would both gain the same amount of energy? If not, which would gain more energy in the process? Approximately how much more (around 4x more, or more than 10x more?)? 

Consider equal MASSES of water and air (air is mostly nitrogen). If both were to increase in temperature by 3 degrees C, would both gain the same amount of energy? If not, which would gain more energy in the process? Approximately how much more (around 4x more, or more than 10x more?)?

Big Hint: Consider / look up the specific heat capacities of water and air / nitrogen.

Very briefly discuss the implications of your above conclusions on climate change / global warming. (For example, as the Earth heats, where is the energy that the Earth gains ending up?)

Answer 1

Water specific heat capacity is: 4.18 J/g*C

Air specific heat capaccity is 1.01 J/g*C

Water can incease if you held everything constant and plug 1 gram for each substance and inserted the change in 3 degrees as 3, you would see that water has the higher specific heat capacity and therefore greater energy increase connected with this.

Another way to check this answer is to use two other equations and compare by holding almost everything else constant: except Pressure. It did not mention that pressure stayed constant and with the ideal gas laws if something changes in one aspect it will reflect in another aspect for the other gas.

PV=nRT

assign, volumes, picking the right R cosntant and watch for same temperature change for each:

3 C = 276.15 K

Water: P*3 = n0.0821(276.15)

n = the moles of 1 g of water : atwt H20= 18.02g/mol

1g * 1mol/18.02g = 0.05549 mol because grams cancelled each other top to bottom.

plug these moles into the equation for water:

P*3= 0.05549*0.0821*276.15

solve for P and you get = 0.419333 atm

now take this pressure and plug in for Air's equation and solve for what n would be:

0.419333*3 =n*0.0821*276.15

For Air n = 0.05549 mol

now with each moles find what the grams will be for the atomic weight for each

water:

18.02 g/mol * 0.05549mol gives you grams at: 0.9999298 g

Air as a molecule is 78 % N, 21% O, 0.9% Argon, 0.1% mostly CO2

so now to get an accurate depiction of the air molecule, multiply the fraction form of each by the atomic weights of each molecule and sum it up and you will have the atomic weight of air.

0.78 * 14.0 = 10.92

0.21*16.00= 3.36

0.009*40 = 0.36

0.001*44.01 =0.04401

Air's atomic weight: 14.68401 g/mol

now we can get grams by the moles solved from earlier 0.05549 mol * 14.68401g/mol mols cancel each other and you have :0.814816 grams of Air.

and

now using the equation

KE = 1/2m*v^2

keep everything constant and compare to see which one yields greater energy:

assign a velocity of 5m/s to each

Water:

KE = 1/2* 0.9999298 (5^2) = 12.499

Air:

KE = 1/2*0.814816*5^2 = 10.1852

and see which one would be connected to greater kinetic energy:

Water has the greater KE at 12.4999 and this checks with the higher specific heat capacity as well so water would have the greater energy increase.

The heat from the earth and the core of the earth is rising and going towards the Ozone layer and causing erosion of the Ozone layer. The Ozone layer is getting thinner and is supposed to protect the earth from some of the sun's rays. This is what is happening with global warming.