Fundamental Laws of Physics

First Law of Thermodynamics

This is the basic conservation law. It basically states that energy can be neither created nor destroyed. Energy can change forms, but none of it is ever lost. For example, a hot cup of coffee has heat energy. If it is left on the table, it will cool, losing energy, but that energy was transfered to the surroundings. This leaves you with cold coffee and a room that is a bit warmer. Careful accounting will show that all of the energy remains, it has just been redistributed.

Similarly, if any chemical reactants exist with a store of chemical energy, such as in hydrogen gas, that energy is conserved upon burning. By burning the hydrogen with oxygen, the chemical energy within is released, creating water and heat. That heat may become dispersed, but it is not lost. By using electricity to drive electrolysis of that same water, it can be returned to its original state of hydrogen gas and oxygen. This will require the same amount of energy be used as was released by the initial burning. And so goes all chemical reactions, nuclear reactions, phase changes, gravitational potential energy, kinetic energy, radiant energy, thermal energy, etc. No process changes the total amount of energy in a closed system, energy only changes between forms.

A basic energy balance for any system (open or closed) could be written as:

change in energy = energy entering the system - energy leaving the system

or, DE = E_in - E_out

For any process where energy is changing form, we must account for each energy type (n) so,

ΣDE_n = (ΣE_n)_in - (ΣE_n)_out

If the system is closed (no energy is entering or leaving), then you have a special case where,

ΣDE_n = 0

The universe is the ultimate closed system, so this formula applies to the universe as a whole. It can also be applied for any process, so that the energy balance can be determined.

Consider this example. On the forth of July, you may be tempted to ignite fireworks, and in so doing, you are affecting an energy system, namely the firework and its surrounding environment. In the case of a bottle rocket, energy of the system for any time interval can be found by:

change in chemical energy + change in kinetic energy + change in gravitational potential energy + change in thermal energy = 0

or, DE_c + DE_k + DE_g + DE_t = 0

And for each DE, DE = E_initial - E_final, so we can expand the prior formula to,

E_ci - E_cf + E_ki - E_kf + E_gi - E_gf + E_ti - E_tf = 0

Separating the initial and final states for each you get:

E_ci + E_ki + E_gi + E_ti = E_cf + E_kf + E_gf + E_tf
or, ΣE_i = ΣE_f

In other words the energy balance at any point in time is, E_c + E_k + E_g + E_t = E_total = constant value. This total energy of the system (E_total) does not change with time. So if you know the amount of chemical energy in the rocket, then you know the total energy of the system, because all three other forms of energy are zero before the rocket is ignited. So then the final state when the rocket has come to rest on the ground will be that the thermal energy is equal to the total energy after all other energy forms are gone. If the rocket is fired straight upward, and you are able to measure the maximum height, then you are able to calculate the maximum gravitational energy of the system. Since the kinetic energy is zero at the point the rocket reverses course, you know the heat energy added to the surroundings up to that point has been the total energy - gravitational energy (E_total - E_g). The kinetic energy just before it hits the ground will be less than the maximum gravitational energy, since air drag will convert some of the kinetic energy to heat before it reaches the ground. By knowing the kinetic energy you can calculate the speed just before impact.

So you can see that conservation of energy is a useful tool for predicting many details of any physical process. It is used in every realm of science. Stars shine by converting nuclear energy from the fusion of hydrogen into helium. This energy in the form of radiant energy, escapes into space, so by the first law, stars cannot shine forever. In space, we observe many remnants of dead stars that exhausted their fuel long ago. The universe has a fixed amount of energy that has been the same since the beginning, and it will contain the same amount in it forever. But that does not mean the universe will remain as it is forever, that is where the second law of thermodynamics comes in.

Second Law of Thermodynamics

While energy is never created nor destroyed, its usefulness is not at all constant. Any closed system with a store of useful energy, will progress towards a less useful or more dispersed energy state. The first law does not specify a direction to energy flow, it only requires that when energy does flow that none is lost. But the second law does specify a direction, which determines what kind of energy transfers are possible.

This brings us to the topic of entropy. Entropy is a measure of the dispersion of energy. The more dispersed or spread out the energy is, the higher its entropy. When energy is concentrated (low entropy) it has the potential to do work. Work is the transfer of energy into a useful form, such as kinetic energy or gravitational potential energy. But whenever energy changes form, some must be dispersed, to drive the process forward.

The second law of thermodynamics is basically summed up by these two statements: A closed system can never experience a decrease in entropy. Energy always flows to a lower energy state. A lower energy state is at higher entropy because the energy is more dispersed in the lower state.

This law can be understood through common sense from life experience. A ball at rest on a hillside does not roll upward, sucking heat out of the environment to balance the change in gravitational potential. Instead, it rolls downhill, adding heat to the environment through friction, as it finally comes to rest at the bottom of the hill. It proceeds this way because energy is flowing to a lower, more dispersed state as it rolls down the hill.

Similarly, a cup of coffee left out over night will be cold. It will not suck heat out of the environment to return to its hot state, no matter how long you wait. Putting that cup in the microwave can return it to its original temperature, but only at the expense of converting energy from low entropy electricity into higher entropy heat.

The second law explains why perpetual motion machines are impossible. Any machine doing work must expend energy, that energy flows to a less useful state and then loses its ability to power the machine. The only way keep any machine running is to continually supply it with a low entropy energy source. This applies to cars, people, stars, everything.

The universe is by definition the ultimate closed system. Encompassing the entire natural order, it too, is bound to the second law. It began at an extremely low entropy state, and entropy has been eroding its energy quality ever since. This represents the most dreadful energy crisis. Trillions of years from now, the universe will run out of useful energy to power stars and life. The total amount of energy will remain constant, but its usefulness will one day be depleted, as the universe approaches its final maximum entropy state.

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updated Oct 15, 2012
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