Energy Loss and Gain in a System

As the ball in the simulation falls, energy transfers from gravitational to kinetic. As it rises, energy transfers from kinetic to gravitational.

Energy is conserved. This means that if we add up the total energy of a system it will always be the same value, unless some energy enters or leaves the system we are tracking.

Turn friction on and observe what happens.

The kinetic energy gradually leaves the ball as it changes into a type of energy called heat.

Heat is the random motion of particles. More heat leads to higher temperatures.

So the internal energy of a system is always conserved, unless energy enters or leaves our system.

The first law of thermodynamics says that the change in internal energy of a system is equal to heat flow into a system plus work done by the system.

$$\Delta E = Q - W$$

\( E \) = total internal energy of a system [J]
\( Q \) = Heat, thermal energy added(+) or removed(-) from system [J]
\( W \) = work done by a system [J]
Example: Compressing a volume of gas does 100 J of work, but at the same time the gas losses 200 J of heat to the surroundings. What is the change in the internal energy of the gas? Will the gas increase of decrease in temperature?
solution $$\Delta E = Q - W$$ $$\Delta E = -200 - 100$$ $$\Delta E = -300\,\mathrm{J}$$ $$\text{The gas will decrease in temperature}$$
Example: A 0.43 kg soccer ball kicked at 10 m/s rolls down a 30 m tall hill. We already solved this problem and got a final velocity of 26.2 m/s for the ball.

When actually performing the experiment we found at the bottom of the hill the ball only has a speed of 20.0m/s. Calculate the energy loss for the ball. How could the ball have lost energy?
solution $$\text{energy difference = calculated - experimental}$$ $$\Delta E = \tfrac{1}{2}mv^{2} - \tfrac{1}{2}mv^{2}$$ $$\Delta E = \tfrac{1}{2}(0.43)(26.2)^{2} - \tfrac{1}{2}(0.43)(20.0)^{2}$$ $$\Delta E = 147.6\, \mathrm{J} - 86\, \mathrm{J}$$ $$\Delta E = 61.6 \, \mathrm{J}$$ $$\text{The energy loss was probably from friction.}$$


Entropy is hard to define because different fields use the term to describe slightly different ideas. The definitions of entropy are all loosely centered around disorder. A high entropy system of particles is not organized. A low entropy system is very orderly, but how do you measure order?

Well, order is whatever you decide. Often order is defined as a concentration of temperature, pressure, volume, or density. Many of these concentrations are able to do work. In the simulation below, the work we want done is rotating the rotor. What state of the system would make the rotor turn?

Click the clear button to remove the particles. Click inside the simulation to add some particles. Try to place the particles in a state that will turn the rotor.

time rate
rotor external power

The system is in high entropy when the particles are evenly spread out. If your system gets in this state, adjust the slider to power the rotor from an external power source. The spinning rotor lowers entropy and puts the system back in a state that can do work.

Entropy plays an important role in thermochemistry, heat transfer, and information theory.

Arrow of Time

If you were to watch a video of th Earth orbiting the sun, it would be difficult to tell if the video was running forwards or backwards. Simple physical systems don't have a clear forwards or backwards.

If you were to watch a glass of water fall off a table, it would be very clear the direction of time. This is because the entropy of the glass of water is rapidly increasing.

The laws of physics are time reversible. Nature behaves the same moving forwards or backwards in time. The only exception is entropy. (also the weak nuclear force)

The second law of thermodynamics states that entropy of an isolated system doesn't decrease over time.

The second law is true for all the different formulations of entropy. As time moves forward entropy either increases or stays the same. Over time things spread out and move towards a balanced equilibrium. These high entropy states have less ability to do work.

A human body as a thermodynamics system keeps it's ability to do work by adding low entropy substances, like food, oxygen, and water. We also lower our entropy by releasing high entropy substances, like carbon dioxide, urine, and feces.

The Earth can be viewed as a thermodynamics system. As time goes on the energy density of Earth spreads out and losses the ability to do work. But the Earth isn't isolated. Low entropy light from the sun is added to our system and lowers our entropy. High entropy infrared light exits our system as the Earth cools.

Inside the Sun, nuclear fusion converts hydrogen into helium and heat. Heat in the form of light strikes the Earth. Sunlight is a low entropy source that is harnessed by plants to produce work. We are able to order our world because the system of Earth is able to get work out of sunlight.