Download Energy and Radiation Reading: p. 25

Energy and Radiation
Reading: p. 25-43
Motivation: Radiant energy from the sun is the ultimate source of all weather—both
terrestrial and space weather.
The sun is powered by nuclear fusion—the melting together of light elements (mostly
hydrogen) to form heavier ones (e.g. helium). This requires extremely high temperatures
(15 million degrees) in order to overcome the strong nuclear forces of repulsion. The
more familiar fission processes involve splitting the nuclei of heavy elements (e.g.
uranium) to release massive amounts of binding energy. Fission is the key to atom
bombs while Fusion is the key to hydrogen bombs.
Facts about the sun:
Center T-27 million deg. F; sfc T~ 10,000 F ;
Center pressure: 250 billion times those on Earth;
Rotates on axis once per month
ENERGY:
Energy= capacity or ability to perform work
Recall from physics that
Work=
Or the summed effect of a force applied over a distance (e.g., pushing a box across the
floor). Clearly one expends energy in doing this, and the work-energy theorem in physics
states that:
Work performed=change in energy
Energy thus represents the potential for doing work, and the concept of potential energy
is foundational in meteorology… it is “stored energy” that is available for performing
work.
Standard example: Water behind a dam-
If the dam breaks or a flood gate is opened, the potential energy quickly is released and
becomes kinetic energy, or energy of motion:
KE=1/2 mv^2
Where V=speed
And m=mass of object/substance in question
Atmospheric Example: thunderstorm situation
The warm/moist air is less dense that the overlying cold/dry air and thus they tend to
“want” to change places
thunderstorms.
The potential energy stored in the vertical temperature and moisture profiles is released in
the form of strong storm updrafts (kinetic energy).
We’ll later quantify the above concept as CAPE: Convective Available Potential Energy
Note in the previous two examples that the potential energy was converted to kinetic
energy, i.e. when the dam breaks, the water level falls (h decreases), but v increases.
Energy is neither created nor destroyed, but is simply converted--- or conserved
Thus, (PE + KE) initial = (PE + KE) final.
In other words, the total energy doesn’t change, but only the partitioning between PE and
KE. In essence, this is the first law of thermodynamics.
TEMPERATURE AND HEATING
As noted last week, temperature is a measure of the average speed of molecules, i.e., it
represents how energetic molecules are… pretty straight-forward! But a bit more
confusing and elusive is the concept of “heat”.
To understand “heat,” we need to bring in the concept of internal energy—the total PE
and KE of molecules… which involves mass.
Thought Experiment:
2 beakers half fitted with water at the same temperature have the same internal energy
and same mass. If we combine them into one, then the internal energy will be 2X, but
T=40 degrees still. Note the difference between T and Internal Energy.
If you place a cold marble in your hand, the marble “heats up”==energy is transferred
from the warm object to the colder one. This is always the case and is the essence of the
second law of thermodynamics—which prohibits the creation of perpetual motion
machines.
The process of energy transfer, noted above, is known as heating. Your book incorrectly
calls it “heat”, as if heat were a quantity. It’s NOT.
There are several kinds of “heat” (p. 28-30), and we’ll now correct the book!
Heat Capacity—you’ve seen this many times; it takes a lot more energy to heat water in a
swimming pool than the ground/concrete nearby! This is the concept of what more
correctly is called heating capacity:
It’s the amount of heating or energy transferred relative to the change in temperature.
In meteorology, you’ll find that we always normalize things by their mass, i.e. “per unit
mass”, because we never measure the actual mass of the air.
{practical analogy: when you’re shopping for an apartment, the absolute price is
important, but more important is the price per square foot, i.e. the total price divided by
the size of the apartment. This allows you to compare different apartments to one
another}
The heat capacity per unit mass is called the specific heat (more appropriately called the
specific heating). It’s the amount of energy (not heat, as your book says), needed to
raise the temperature of one gram of a substance by one degree Celsius.
See Table 2.1 (p.28) for a comparison of many substances.
Latent heating—This tends to be a bit confusing, yet is hugely important in meteorology!
Latent “heat” is the amount of energy (not heat energy, as your book states) needed to
change the phase or state of a substance—from a gas to a solid, liquid to gas, etc…
But why is it called latent?
Consider an everyday example—evaporation (state changes from a liquid to a gas).
At the drop’s surface, molecules are constantly escaping if the relative humidity of the
surrounding air is <100% (more on this soon). Those molecules leaving are the most
energetic…
The average KE of the molecules left behind decreases
T
decreases.
Where does the energy needed to evaporate the water come from? It can come from the
drop, air, etc. A good example is our skin—it gives up energy to evaporate perspiration
on a hot day.
Now, where does the energy actually go? It is carried away by the molecules that leave
the water drop surface, and this is “stored” for release later. It is thus “latent” or
“hidden”. Note that the Relative Humidity of the air has increased (context of
thunderstorms). When the water molecules condense (return to the liquid phase), they
impart their energy to the water drop and thus increase its temperature.
This “release of latent heat” produces a rise in T that can be measured by a thermometer,
and this is called sensible heating (not heat, as your book says). The release of latent
“heat” in clouds is key to storms and precipitation.