More on Energy and Expansion

Ok, we have been pounding on the idea that heat is really just kinetic energy, and we are going to take it a little farther gain, hopefully in the pursuit of clarity.

As we know from the previous blog posts, the heat of a substance is the motions of its molecules. At some point of low temperature it’s obvious that there must be an end point, since if there is no movement of any of the molecules the effective energy is zero. That zero point is known as absolute zero and is equal to zero Kelvin. Typically in physics when referring to temperature the Kelvin scale is used. This is convenient since the standard equation for the energy of any system is based squarely on Kelvin.

E=2x10^-23T^k

E=Energy, T=Temperature in (k) Kelvin

No need remember this equation just the simplicity of its implications. Temperature is just the kinetic energy…when at the same temperature the energy of the molecules and atoms of the air are the same as those in a piece of paper, or a desk, or a pillow. The difficulty part is that these energies have to be measured per molecule and this fact eluded great minds for centuries, but the byproducts are intuitive. It is this very simplicity that some physicists like Richard Muller have pointed out is the “beauty” of physics. It’s not a traditional beauty; it’s the beauty of the simplicity, the beauty of the fact that when striped of its erudite mathematics the core principles are clear and reasonable.

To take ideas we discussed in the previous blog a step farther let’s apply what we have learned about increasing the energy or heat of a substance to solids. We considered that due to the low mass of atoms like helium, at room temperature in order to comply with the zeroth law of thermodynamics their velocity must be very high. When confined in a container like a bloom their high velocity causes them to collide with vigor and throw each other apart. The result is the average density of a helium balloon is less then that of the atmosphere allowing it to rise. If you place a helium balloon on a pool of liquid hydrogen (20.28K,-252.87Celcius) this will cause the helium atoms to cool and the result is quite clear as the balloon will contract and become smaller. Again this is because the velocity of the helium atoms has decreased as they cool and they then collide less frequently and with less energy.

The effect of the increase of temperature and kinetic energy is also relevant in solids. Typically solids expand by 1 part in 1000 to 1 part in 100,000 for every degree Kelvin (side note 1 degree Celsius = 1 degree Kelvin) increase. This may sound like a nominal amount but if one considers a structure like a suspension bridge the implications are necessary to consider. A bridge like the Verrazano-Narrows Bridge in Brooklyn which has a main span of over 4000 ft experience temperature swings of up to 30 degree Kelvin. The by product of this is an expansion or contraction of up to 2 feet. In addition the cables that transmit the weight of the bridge also contract or expand with temperature causing the center of the bridge to be 12 ft higher in the winger then the summer.

Another interesting byproduct of this is induced by the much hyped global warming. We have all heard over and over ad nauseum of the alarmingly imminent rise in sea-level due to global warming. The common misconception is that solely the glacial melting will increase the overall volume of the oceans thereby pushing up the sea level catastrophically. And although this could contribute nominally to a rise in global sea levels the sneaky culprit may really be the byproducts of heat expansion. The volume expansion of water is 2x10^-4 per degree Kelvin. Given this the math works out such that with an average ocean depth of 12,000 ft a rise in temperature of 5 degrees Kelvin (9 Fahrenheit) would equate to a rise in average sea level of approximately 6 feet. This rise caused by heat / kinetic energy induced expansion is enough to overwhelm most of the populated areas of Florida. (There are some details on quirky dynamics of water around 4 degrees Celsius that modify the more specific outcome of these equations, but the end result is still enough to account for flooding Florida’s populated areas and many other littoral populaces.)