The Second Law of Thermodynamics
Rudolf Julius Emanuel Clausius (German physicist and mathematician, 2 January 1822 - 24 August 1888) made the original statement of the second law of thermodynamics in 1850: Heat cannot of itself pass from a colder body to a hotter body. William Thomson Kelvin (British mathematician and physicist, 1824–1907) applied this law to the operation of heat engines. Heat engines require a source of heat at a high temperature and a destination for used heat at a low temperature. Kelvin’s statement says: If there is no temperature difference between the source and the destination then no heat engine can run and do useful work. That includes all of us, since biological systems work like heat engines. The two statements are equivalent to each other.
Originally the second law of thermodynamics was about heat. Engineers of the 19th century tried to make steam engines more efficient. The principles they discovered apply to all systems that extract energy from heat and perhaps use it to do useful work. In the course of discovering precisely how much work heat can do, engineers developed the concept of entropy. To them entropy measured the inability of heat energy to do work.
Later others extended the concept of entropy. In general, we can now say that entropy is a certain kind of disorder, a measure of the number of ways things can get out of their proper arrangement. First, we will explain how this applies to heat.
Once physicists and chemists understood that gases contain small particles called atoms or molecules, they could relate heat to disorder. The hotter the gas, the faster the particles move. They bump into each other and bounce off the walls of the containing vessel. For example, in a steam boiler, water vapor molecules fly about randomly in all directions.
A steam engine has special containing vessels called cylinders, with a movable wall at one end called a piston. When the molecules of steam bounce off the piston, they exert pressure on it. When the piston moves back in response to the pressure, the molecules give up some of their energy and move more slowly. The moving piston is usually attached to a crankshaft and flywheel, so its motion can do useful work. In this way a steam engine converts some of the disorganized motion of the water molecules into the organized, reciprocating motion of a piston and the rotary motion of a flywheel. The engine extracts energy from steam, cooling the steam and making the water vapor molecules move more slowly.
The molecules don’t stop short and fall out of the engine’s cylinders, however. No engine can get all the energy of motion from the molecules, because they are too disorganized when they are hot. Some steam engines discharge the cooled steam into the atmosphere. Others condense the cooled steam and return it to the boiler, but they depend on air or water circulation to cool the condenser. Either way, some of the heat is wasted.
To heat the water the engine has to burn fuel. Typical fuels have carbon and hydrogen atoms highly organized in large organic molecules, and air has oxygen atoms paired off in oxygen molecules. Burning breaks up the large molecules, mixes the atoms with oxygen, and scatters many small molecules of water vapor and carbon dioxide in the atmosphere. Many fuels leave a residue of ashes or produce smoke containing small particulate matter. In summary, heat engines produce some organized motion in their moving parts, at the expense of the much more disorganized motion of waste materials dispersed in the environment.
Entropy is a measure of the disorder before and after the heat engine runs. If there is a place for each particle, then they are disordered if some of them are in the wrong places. Entropy depends on the number of different ways particles can be arranged in the wrong places. We will describe this dependence later. Entropy increases slowly if the number of different wrong arrangements increases rapidly.
Physics cannot calculate the total amount of entropy in the environment. It analyses the difference in entropy before and after a process occurs or an engine goes through one cycle. The difference in entropy is the heat energy that moves from a high-temperature source to a low-temperature destination, divided by an appropriate absolute temperature. The appropriate absolute temperature for calculating entropy always lies between the high temperature of the heat source and the low temperature of the heat’s destination. The two original versions of the second law of thermodynamics are equivalent to a much more general statement, as follows: The sum total of entropy never diminishes. In any process the entropy either increases or stays constant. If the entropy stays constant, the process is reversible. All other processes are irreversible.
“Murphy’s Law” is a humorous axiom warning that anything that can go wrong will go wrong. The law of the non-decrease of entropy is not the same as Murphy’s Law, nor does it simply mean that bad things often happen. Physicists, chemists, and engineers can calculate entropy in simple situations. Other interpretations that apply the idea of entropy to things in general are no more than pessimism, the tendency to notice the bad more than the good.
Physics cannot analyse any arbitrary kind of disorder. For instance, it would be difficult to calculate the entropy schoolchildren produce by talking in class, chewing gum, or running in the halls.
People understand the second law of thermodynamics in an intuitive way. Organizing or imposing order on a mess involves separating dissimilar things. Dirt enters a house “all by itself,” blown in with the wind or riding in on people’s clothes and shoes. Things get misplaced as thoughtless people use them and then put them down anywhere without cleaning them or putting them back where they belong. Things get disorganized when we fail to pay attention to them. We have to think and work to get things organized. Ask any housekeeper. You will learn that houses become disordered spontaneously. Putting a house in order requires the work of an intelligent person.
After an intelligent housekeeper puts the house in order the next task may be preparing lunch. Food preparation always requires separating edibles from garbage. Plants grow well in soil fertilized with manure, but someone must harvest them and wash them before anyone can eat them and stay healthy. There are many separate tasks in gathering and preparing food. Engineers have invented machines to do some of the tasks but not all. Machines can core apples, but it still takes eyes and hands to throw out all the bad ones. When we buy prepared food, we don’t see the legions of intelligent workers who made the purchase possible. The combination of workers and machines is a very complex, intelligent filter. The last part of the filter is the diners, who still may have to sort out bones, shells, rinds, and pits. If entrepreneurs could replace all of that with a simple filter or an automatic machine that doesn’t require intelligent supervision, they would have done so and grown rich long ago. If sometime in the future almost all of the process is automated, that will be the result of very clever creative design.
Originally the second law of thermodynamics was about heat. Engineers of the 19th century tried to make steam engines more efficient. The principles they discovered apply to all systems that extract energy from heat and perhaps use it to do useful work. In the course of discovering precisely how much work heat can do, engineers developed the concept of entropy. To them entropy measured the inability of heat energy to do work.
Later others extended the concept of entropy. In general, we can now say that entropy is a certain kind of disorder, a measure of the number of ways things can get out of their proper arrangement. First, we will explain how this applies to heat.
Once physicists and chemists understood that gases contain small particles called atoms or molecules, they could relate heat to disorder. The hotter the gas, the faster the particles move. They bump into each other and bounce off the walls of the containing vessel. For example, in a steam boiler, water vapor molecules fly about randomly in all directions.
A steam engine has special containing vessels called cylinders, with a movable wall at one end called a piston. When the molecules of steam bounce off the piston, they exert pressure on it. When the piston moves back in response to the pressure, the molecules give up some of their energy and move more slowly. The moving piston is usually attached to a crankshaft and flywheel, so its motion can do useful work. In this way a steam engine converts some of the disorganized motion of the water molecules into the organized, reciprocating motion of a piston and the rotary motion of a flywheel. The engine extracts energy from steam, cooling the steam and making the water vapor molecules move more slowly.
The molecules don’t stop short and fall out of the engine’s cylinders, however. No engine can get all the energy of motion from the molecules, because they are too disorganized when they are hot. Some steam engines discharge the cooled steam into the atmosphere. Others condense the cooled steam and return it to the boiler, but they depend on air or water circulation to cool the condenser. Either way, some of the heat is wasted.
To heat the water the engine has to burn fuel. Typical fuels have carbon and hydrogen atoms highly organized in large organic molecules, and air has oxygen atoms paired off in oxygen molecules. Burning breaks up the large molecules, mixes the atoms with oxygen, and scatters many small molecules of water vapor and carbon dioxide in the atmosphere. Many fuels leave a residue of ashes or produce smoke containing small particulate matter. In summary, heat engines produce some organized motion in their moving parts, at the expense of the much more disorganized motion of waste materials dispersed in the environment.
Entropy is a measure of the disorder before and after the heat engine runs. If there is a place for each particle, then they are disordered if some of them are in the wrong places. Entropy depends on the number of different ways particles can be arranged in the wrong places. We will describe this dependence later. Entropy increases slowly if the number of different wrong arrangements increases rapidly.
Physics cannot calculate the total amount of entropy in the environment. It analyses the difference in entropy before and after a process occurs or an engine goes through one cycle. The difference in entropy is the heat energy that moves from a high-temperature source to a low-temperature destination, divided by an appropriate absolute temperature. The appropriate absolute temperature for calculating entropy always lies between the high temperature of the heat source and the low temperature of the heat’s destination. The two original versions of the second law of thermodynamics are equivalent to a much more general statement, as follows: The sum total of entropy never diminishes. In any process the entropy either increases or stays constant. If the entropy stays constant, the process is reversible. All other processes are irreversible.
“Murphy’s Law” is a humorous axiom warning that anything that can go wrong will go wrong. The law of the non-decrease of entropy is not the same as Murphy’s Law, nor does it simply mean that bad things often happen. Physicists, chemists, and engineers can calculate entropy in simple situations. Other interpretations that apply the idea of entropy to things in general are no more than pessimism, the tendency to notice the bad more than the good.
Physics cannot analyse any arbitrary kind of disorder. For instance, it would be difficult to calculate the entropy schoolchildren produce by talking in class, chewing gum, or running in the halls.
People understand the second law of thermodynamics in an intuitive way. Organizing or imposing order on a mess involves separating dissimilar things. Dirt enters a house “all by itself,” blown in with the wind or riding in on people’s clothes and shoes. Things get misplaced as thoughtless people use them and then put them down anywhere without cleaning them or putting them back where they belong. Things get disorganized when we fail to pay attention to them. We have to think and work to get things organized. Ask any housekeeper. You will learn that houses become disordered spontaneously. Putting a house in order requires the work of an intelligent person.
After an intelligent housekeeper puts the house in order the next task may be preparing lunch. Food preparation always requires separating edibles from garbage. Plants grow well in soil fertilized with manure, but someone must harvest them and wash them before anyone can eat them and stay healthy. There are many separate tasks in gathering and preparing food. Engineers have invented machines to do some of the tasks but not all. Machines can core apples, but it still takes eyes and hands to throw out all the bad ones. When we buy prepared food, we don’t see the legions of intelligent workers who made the purchase possible. The combination of workers and machines is a very complex, intelligent filter. The last part of the filter is the diners, who still may have to sort out bones, shells, rinds, and pits. If entrepreneurs could replace all of that with a simple filter or an automatic machine that doesn’t require intelligent supervision, they would have done so and grown rich long ago. If sometime in the future almost all of the process is automated, that will be the result of very clever creative design.