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# 2.11 Probability, Thermal Equilibrium, and Entropy

K

Krish Gupta

Daniella Garcia-Loos

### AP Physics 2ย ๐งฒ

61ย resources
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In this section, we finally get to the 2nd law of Thermodynamics. This section is heavy on theory and understanding of math rather than its application. This section might be one of the hardest to understand because it deals with intangible quantities, so just try your best๐ฅ
Entropy is disorder. That is the most surface level definition ever. Some people also define entropy as molecular freedom. You can also define entropy as randomness or lack of predictability. Also the universe favors entropy. The universe wants more disorder๐

## Entropy

The 2nd Law of Thermodynamics states that the entropy of the system and its surroundings will never decrease. So the entropy or disorderness can either stay the same or increase.
Calculating entropy is not tested on the exam but we will learn briefly about it anyways in case you study it in college. Entropy at a point is the ratio between heat and temperature and is represented by the letter S. S=Q/T
There are two types of thermodynamic processes we can think about based on entropy.
1. Reversible - these processes can be done forward or backwards. These processes do not increase the entropy of the universe: entropy stays constant. A famous example of this is the carnot cycle. Carnot cycles are the most efficient. They consist of 2 adiabatic processes and 2 isothermal processes. The gas is returned to its original state and no increase in entropy occurs.
2. Irreversible - these processes can only be done in one direction. The entropy of the universe does increase due to irreversible processes. All real life engines perform irreversible processes. Heat pumps and refrigerators are some of the most common examples.
In thermodynamics, the tendency of an isolated system to move toward a state of higher disorder is known as the "arrow of time."
• This tendency can be described using the concept of probability, which is a measure of the likelihood of an event occurring.
• In an isolated system, the probability of any given state occurring is proportional to the number of ways that state can be reached.
• States with higher disorder (or more randomness) typically have more ways that they can be reached, so they have a higher probability of occurring.
• This means that, over time, an isolated system will tend to move toward states with higher disorder, because those states are more likely to occur.
• The second law of thermodynamics states that the total entropy (a measure of disorder) of a closed system will always increase over time, which is a consequence of this tendency toward higher disorder.
• ## Heat Engines and Refrigerators

These topics are not quite tested on the AP exam anymore but used to show up on the exam several years ago and are taught in several college courses so we will quickly go over them.
1. Heat Engines - heat is imputed from a high temperature then some is converted to work and the rest in released as low temperature ๐ฅ
1. Refrigerators/Heat Pumps - work is done in conjunction with low temperature to kick out higher temperature heat ๐ง
Here are some key points about heat engines:
• A heat engine is a device that converts heat energy into mechanical work.
• Heat engines operate on a cycle, which involves the transfer of heat from a hot reservoir to a cold reservoir through the engine.
• The hot reservoir is typically a source of high-temperature heat, such as burning fuel or steam from a boiler. The cold reservoir is typically the environment, which is at a lower temperature.
• Heat is used to do work by expanding a gas or fluid, such as steam in a steam engine.
• The efficiency of a heat engine is the ratio of the work it does to the heat it receives. The efficiency is limited by the temperature difference between the hot and cold reservoirs.
• Examples of heat engines include steam engines, internal combustion engines, and gas turbines.
Here are some key points about heat pumps and refrigerators:
• A heat pump is a device that moves heat from one location to another. It can transfer heat from a cold location to a warm location (such as a heating system), or from a warm location to a cold location (such as an air conditioner).
• A heat pump uses a small amount of mechanical work to transfer a large amount of heat. It is more efficient than a heat engine because it can operate at a higher temperature difference between the hot and cold reservoirs.
• A refrigeration system is a type of heat pump that is used to cool a space or to preserve perishable goods. It works by removing heat from the cooled space and transferring it to the environment.
• A refrigeration system typically consists of a compressor, a condenser, an expansion valve, and an evaporator. The refrigerant (a fluid that can easily change between a gas and a liquid) absorbs heat in the evaporator and releases it in the condenser. The compressor raises the pressure of the refrigerant, which increases its temperature. The expansion valve lowers the pressure of the refrigerant, which lowers its temperature.
• The efficiency of a refrigeration system is limited by the temperature difference between the cold and hot reservoirs and by the properties of the refrigerant.
Example Problem:
Explain how the second law of thermodynamics is related to the state function called entropy and how entropy behaves in reversible and irreversible processes. In your explanation, provide an example of a process that is reversible and another that is irreversible, and explain how the entropy changes in each case.
To answer this question, you could describe the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. Define entropy as a measure of the disorder or randomness of a system, and explain how it is a state function, meaning that it depends only on the state of the system and not on the path taken to reach that state.
An example of a reversible process, such as a gas expanding and contracting in a cylinder, and explain how the entropy changes in a reversible process. Give an example of an irreversible process, such as a gas expanding into a vacuum, and explain how the entropy changes in an irreversible process. Explain how the increase in entropy in irreversible processes is what drives the arrow of time and why the past and future are fundamentally different.
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