Re: How much energy is needed to raise the temp of 1 cm3 air by 1 centigrade

The question: "How much energy is needed to raise the temp of 1 cm3 air by 1 centigrade? Im'e trying to devise energy saving tips for my home, and would like to know if I am going in the right direction! Also, if eg:0.05w is needed for 1cm3, does that mean 0.1w is needed to heat 2cm3 by 1 centigrade? finally, is the energy required to heat 1cm3 of air from say 4 to 5 celcius the same as heating it from 19 to 20 celcius?"

I am going to answer your 1st and 3rd questions together.

Look at the table at (Dry) Air Properties at Engineering Toolbox. (Some of the numbers are different for moist air, which you can see at this other page at Engineering Toolbox. For illustration we will assume dry air.)

The third column of the first table shows the specific heat capacity of air at various temperatures. You will notice that there are slight differences depending on temperature. But that's only part of the story! Something else that varies with temperature is the density, and the computation of energy involves the mass of the air, so that the density is important.

Let's take your examples. It turns out that your 2 chosen temperatures have the same c_p, to the 4 significant digits shown. But the density of (dry) air at 4^oC is about 1.274 kg/m³ while at 19^oC is about 1.208 kg/m³, assuming the air pressure is 29.92 inches Hg (Which is one normal atmosphere of pressure.). (There is a nice online calculator at Shelquist Engineering, which you can use to find the densities at various pressures and relative humidities!) In the calculations below recall that the size of a Celcius degree is the same as that of a Kelvin degree.

The calculation is: Energy = c_p * temprature change * density * volume, and it is important to keep the units consistent!

So, at 4^oC we have
Energy1 = 1.005 kJ/kg.C * 1C^o * 1.274 kg/m³ * 1.0*10^-6 m³ = 1.280*10^-6 kJ
Let's do the same calculation for air at 19^oC:
Energy2 = 1.005 kJ/kg.C * 1C^o * 1.208 kg/m³ * 1.0*10^-6 m³ = 1.214*10^-6 kJ

So, due primarily to the reduced density at the higher temperature, it takes less energy to heat the cubic centimeter of air at 19^oC than at 4^oC .

Now for your 2nd question: The answer is "yes". If one doubles the quantity of air then the energy required to heat it also doubles. This holds for any multiple of the base quantity.

John Link, MadSci Physicist