Second Law of Thermodynamics and Entropy

Alyssa Candelmo (acandelmo6)

Short Description of Topic

The Main Idea

Entropy represents the quantity of the unavailability of a systems thermal energy to be converted into mechanical work. The entropy of the system can also be described as the systems level of disorder or randomness. The more entropy a system has, the more random it will be. The second law of thermodynamics states that the entropy of the universe will always increase over time. The second law also states that change in the entropy of the universe will never be negative. Essentially, through the discovery that heat can not spontaneously flow from a colder body to a hotter body, physicists also discovered that is impossible to complete any physical process without the loss of some useable energy. As time goes on, randomness can only increase.

A Mathematical Model

Boltzmann's Equation: ΔS = K lnΩ

Where ΔS is the change in entropy of the system

K is the Boltzmann's Constant (or 1.38065 × 10‾²³ J/K)

Ω is the number of microstates corresponding to a given macro state

The Second Law of Thermodynamics: ΔS = ΔQ/T

Where ΔS is the change in entropy of the system

ΔQ is the change in heat of the system,

T is the temperature at the point where the heat transfer took place

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

How is this topic connected to something that you are interested in?
How is it connected to your major?
Is there an interesting industrial application?

History

Contributors in the Development of the Second Law:

Nicholas Léonard Sadi Carnot (1 June 1796 – 24 August 1832)
- Considered to be the father of Thermodynamics
- Major Scientific Contributions:
  - Carnot heat engine
  - Carnot theorem
  - Carnot efficiency
- His research was centered around learning if the work available from a heat source was limited, and whether the efficiency of a heat engine could be improved upon by replacing steam with a different substance

Rudolf Clausius ( 2 January 1822 – 24 August 1888)
- German Physicist
- Developed the Clausius statement, which states that in general, heat can not flow spontaneously from a low temperature to a high temperature
- Wrote a famous paper titled "On the Moving Force of Heat and the Laws of Heat which May be Deduced Therefrom"
  - Pointed out differences between the concept of conservation of energy
  - Stated that assumptions about the Caloric theory were incorrect
- Presented the idea of Entropy and named it as such
- Was known for taking a mathematical approach to physics

William Thompson (26 June 1824 – 17 December 1907)
- Also known as First Baron Kelvin
- Mathematical physicist and engineer
- Formulated the Kelvin Statement, which states that there is no way to convert all of the energy in a given system into work without losing energy
- Developed the vortex theory of the atom
- In addition to his contributions to thermodynamics, he also created the Kelvin scale

Constantin Carathéodory (13 September 1873 – 2 February 1950)
- German mathematician of Greek origin
- Principle of Caratheodory
- Took on thermodynamics with a mathematical axiomatic foundation
- Created his own version of the Second Law of Thermodynamics by stating that "In the neighborhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state."
- Used differential equations and Pfaffian expressions to prove the existence of entropy