# Thermodynamics

## Thermodynamics and heat engines

A necessary and difficult topic to understand energy is thermodynamics. This topic deals with conversion of heat energy to work or mechanical energy and the fundamental limits in these conversions.

On mental model that may help is that hot gases have molecules traveling in all directions. To make a heat engine, the kinetic energy of these molecules flowing in all directions must be converted to a kinetic energy moving in only one direction. Since some of the gas energy isn't in the right direction, some of it isn't used and reduces the efficiency.

## Concepts

* Temperature
* Heat
* Laws of Thermodynamics
* Energy Quality

## Temperature

* Measure of the internal energy in a system or material
* This energy is the motion, vibration, or rotation of atoms and

  molecules

## Heat

* Heat is the flow of this energy from one area to another
* Conduction
* Convection
* Radiation

## Heat Engines

* The heat engine is a mathematical model
* Takes the heat (flow) between two thermal resevoirs and converts some of

  that heat to work
* Heat can come from combustion or natural sources of heat
* Heat engines have limits to efficiency dictated by the laws of

  thermodynamics
* Maximum possible efficiency is related to the temperature of the hot

  reservoir and of the cold reservoir

## Heat Engine

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSfiR88zL7pfd0W3%2Fheat_engine_vector.png?generation=1565805387664156\&alt=media)

## Carnot Heat Engine

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSfrMwweRFp6XIWL%2Fcarnot_cycle.png?generation=1565805387369260\&alt=media)

* Heat is used to expand a gas and do work and heat is removed during

  the compression of the gas.

## Power plant

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSftYWabQOu4UQl_%2Fheat_engine_plant.jpg?generation=1565805387706964\&alt=media)

## Power plant

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSfvlZ2SC5L9UWZl%2Fcoal_plant_cooling_towers.jpg?generation=1565805372814686\&alt=media)

## Zeroth Law of Thermodynamics

* If two systems are each in thermal equilibrium with a third system,

  they are also in thermal equilibrium with each other.
* Real world example: Coffee gets cold, ice cream melts

## First Law of Thermodynamics

* Energy is conserved
* Energy cannot be created or destroyed
* "You can't get something for nothing"

## First Law Efficiency

* Most commonly used measure of efficiency
* Useful energy out divided by total energy in

## Second Law of Thermodynamics

* The amount of entropy (disorder) in a closed system always increases
* Heat flows spontaneously from hot to cold
* "You can't break even"

## Second Law Efficiency

* First law efficiency divided by best possible efficiency dictated by

  the second law
* It isn't always obvious what the best possible second law efficiency is

## Third law of Thermodynamics

* The entropy of a perfect crystal at absolute zero is exactly equal to

  zero.
* When we make calculations using the second law, we use the kelvin

  temperature scale which starts at absolute zero.

## Temperature Scales

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSfxeQDvBhXFBk9u%2Ftemperature_scales.jpg?generation=1565805372976009\&alt=media)

## Entropy

* Measures the disorder in a system
* Is related to the number of microstates

## Quality

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSfzJVdw6j3cRszS%2Fmechanical_thermal.jpg?generation=1565805372614885\&alt=media)

## Quality

![](https://3554776031-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LmGGORDQh7HH9qQoHfr%2F-LmGGPt2R6sTJWvHF8E1%2F-LmGGSg07kRn4xmHuGs1%2Fheat_engine.jpg?generation=1565805387927191\&alt=media)

## Thermodynamic limit to heat engine

* Carnot derived the upper limit of efficiency for a heat engine

  $$\eta = 1 - \frac{T\_C}{T\_H}$$
* This law dictates the maximum possible efficiency for power plants
* Some of the heat must be released into the environment

Questions:

* what happens when T\_C goes to zero?
* what happens when T\_C and T\_H are close to each other?

## Multiplication of efficiencies

* When we want to know the efficiency of a process with many steps, we

  multiply the efficiencies at each step to get the total.

  $$\eta\_{total} = \eta\_1 \cdot \eta\_2 \cdot \eta\_3 \cdots$$

## Heat Engines
