15.7 Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying
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When you toss a coin a lot, heads and tails come up in equal numbers.
The different ways in which the second law of thermodynamics is formulated tell what happens.
It is a matter of overwhelming probability.
Order is more likely than disorder.
The drops fall in a disorganized manner both in time and space when you watch a rain storm.
They never fall in straight, orderly rows.
There are many more disorderly ways for rain to fall than an orderly one.
We will look at some random processes, starting with coin tosses.
Each coin has the ability to land on heads or tails.
We are only concerned with the total heads and tails, not the order in which heads and tails appear.
We call them macrostates.
It doesn't specify the order in which heads and tails occur or which coins are heads or tails.
A system of 5 coins has 6 possible macrostates listed.
Some macrostates are more likely to occur than others.
There is only one way to get 5 heads, but there are other ways to get 3 heads and 2 tails, making the latter more probable.
Table 15.3 lists all the ways in which 5 coins can be thrown, taking into account the order in which heads and tails occur.
The macrostate of 3 heads and 2 tails can be achieved in 10 ways and is 10 times more probable than the one with 5 heads.
It is likely to have 2 heads and 3 tails.
It is equally likely to get 5 tails as it is to get 5 heads.
All of the conclusions are based on the assumption that each microstate is equally probable.
With coin tosses, the coins must not be asymmetric in a way that favors one side over the other.
The analysis will be incorrect if the assumption that all microstates are equally probable is valid.
5 heads or 5 tails are the two most orderly possibilities.
Only 2 out of 32 possibilities are likely to be true.
3 heads and 2 tails are the most disorderly possibilities.
20 out of 32 possibilities for the 3 heads and 2 tails and its reverse are most likely to be disorderly.
It is very likely that we will get a less orderly array if we start with an orderly array like 5 heads and toss the coins.
If you start with an orderly state, there is a tendency to go from order to disorder.
It is unlikely that the reverse will happen.
For larger systems, this result becomes dramatic.
If you have 100 coins, think about what will happen if you have just 5.
The most orderly arrangements are 100 heads or 100 tails.
50 heads and 50 tails are the least orderly.
To get the most orderly arrangement of 100 heads, there is only one way.
There are 100 ways to get the next most orderly arrangement of 99 heads and 1 tail.
The least orderly arrangement is 50 heads and 50 tails.
The number of microstates for each macrostate is listed in Table 15.4.
The number of different ways 100 coins can be tossed is an impressively large.
There is a good chance that we will get a less orderly macrostate if we start with an orderly macrostate.
We will never get back to the most orderly macrostate if we keep tossing the coins.
This period is 1 trillion times longer than the age of the universe, and so the chances are zero.
There is an 8% chance of getting 50 heads, a 73% chance of getting from 45 to 55 heads, and a 96% chance of getting from 40 to 60 heads.
It is highly likely that there is disorder.
Imagine applying this approach to a small sample of gas.
An ideal gas at 1.0 atm has a huge number of atoms.
Each macrostate has many microstates.
This means that there are many ways in which the atoms in a gas can be arranged.
A random distribution of atoms in space with a Boltzmann distribution of speeds in random directions is the most likely conditions for a gas.
This is the most disorganized and disorganized condition we can imagine.
One type of very orderly and structured macrostate has all of the atoms in one corner of a container with the same velocities.
It is very unlikely that this will ever happen because there are very few ways to do it.
It is not likely that we have a law saying that it is impossible, which has never been observed to be violated.
It is very unlikely that the atoms or molecule will end up in one corner of the container.
It will return to normal conditions if left alone, because they are immensely more likely.
The ordered condition has low entropy and the disordered one has high.
With a transfer of energy from another system, we could force all of the atoms into one corner, but at the cost of an increase in the universe's entropy.
If the atoms start out in one corner, they will spread quickly and never return to their original state.
Entropy will increase.
It is unlikely that the sample of atoms will decrease the entropy.
Order is more likely than disorder.
The most probable states are disorder and high entropy.
The more likely a state is, the greater its entropy.
The basic idea of the second law of thermodynamics is that it either stays the same or increases in every process.
The phenomenon is caused by the small probability of a decrease due to the larger number of microstates in systems with greater entropy.
This outcome is so unlikely that it will never be observed.
If you toss 100 coins with 60 heads and 40 tails, you will get the most likely result, 50 heads and 50 tails.
The number of microstates is labeled in Table 15.4 for the 100 coin toss.
The subscript is for the initial 60 heads and 40 tails state and the final 50 heads and 50 tails state.
We have moved to a less orderly situation because of the increase in entropy.
The initial state of 60 heads and 40 tails is not impossible for further tosses.
There is a small chance of that happening.
We get if we calculate the decrease in entropy to move to the most orderly state.
There is a chance of this happening.
It's not likely that there will be a small decrease in entropy, but it's not likely that there will be a larger decrease.
The probabilities imply that a decrease in the system's entropy is impossible.
There would be a decrease in the amount of ice in the environment for heat transfer to occur spontaneously.
A decrease of this size is impossible because it corresponds to about a chance.
It is not possible to refreeze melted ice.
Evaluate the situation to find out if there is something going on.
Draw a diagram of the system showing energy flow.
Identifying the unknowns will help determine exactly what needs to be determined in the problem.
A written list can be useful.
A list of what can be inferred from the problem can be made.
You need to know the temperature at which the process takes place.
Identifying the initial and final states is important.
The unknown is the appropriate equation for the quantity to be determined.
It is possible to determine the change in entropy between states by calculating it for a reversible process.
To get numerical solutions complete with units, substitute the known value along with their units into the equation.
For any real process, total entropy should be constant or increased.
Running water or the heat of the Sun are examples of thermodynamics external energy supplies.
The first law of thermodynamics states that work is known as a heat engine.
The isobaric is the sum of all work done on or by the isochoric, isothermal and adiabatic processes.
Both and are energy in transit, only they affect pressure, volume, temperature, and heat, which is an independent quantity capable of being transfer.
The internal energy of a system depends on the environment, so work will be a positive value.
The system's state and how it reached it.
One of the important implications of the first law of in practice is that processes of loss of energy do not work.
The second law of thermodynamics has two expressions, one of which is the ability to heat an interior space.
A refrigerator is a heat pump and takes warm ambient air to chill it.
Cyclical processes return to their original state at the end of the Second Law cycle.
The ratio of Entropy is zero in a reversible process; it increases in a work output divided by the amount of energy input.
The ultimate fate of the universe is likely to be terms of the Otto cycle, which is a repeating sequence of equilibrium, where universal processes that convert heat into work.
A closed system has a thermodynamics restated disorder.
The Carnot cycle is the most 15.7 Statistical Interpretation of an efficient cycle.
Disorder is more likely than order and any engine that uses the Carnot cycle enjoys the statistically.
Carnot engines are ideal engines, in reality, no can be written as engine achieve Carnot's theoretical maximum efficiency, since dissipative processes, such as friction, where is Boltzmann's Carnot cycles without heat loss are a natural logarithm of the number of possible at absolute zero, but they have never been seen in microstates corresponding to the given macrostate.
There is clearly a correlation between thermodynamics energy andConservation of Energy.
One method of converting heat transfer into doing work transit is to store the energy in the body for later use.
Give an example of each type of energy, and state expands, doing work on a piston, as shown in the figure specifically how it is either in transit or resides in a below.
Give an explanation of how food energy can be seen as potential energy.
Take a look at the types of energy transferred to your body in each of the following: basking in sunlight, eating food, and riding an elevator to a higher floor.
A lot of effort, time, and money has been spent in the quest for the so-called perpetual-motion machine, which is defined as a hypothetical machine that operates or produces useful work indefinitely and/or a hypothetical machine that produces more work or energy than it consumes.
Explain, in terms of heat engines and the first law of thermodynamics, why or why not such a machine is likely to be constructed.
We usually say that for an isothermal process.
A rapidly expanding gas' temperature decreases.
Dissipative mechanisms are a cause of irreversibility.
Think about the drinking bird at the beginning of the section.
Does the second law affect the amount of work?
If a real process occurs over a short time, it may be nearly adiabatic.
In some Northern European nations, homes are being built without heating systems.
You are driving a car up a mountain.
It is still warm in these houses to raise a car that large.
A million joules would be required for a possible meters.
The refrigerators, air conditioners, and heat pumps pump gas.
Driving up Pike's Peak is the most cost-effective way to travel up the mountain.
Definitions of efficiency vary depending on how energy refutes the claim.
The store has many refrigerators and freezers.
The same bricks are in a disorganized pile.
An example of a macrostate is given.
The process of thermodynamics transfer takes place in the environment.
Problem-Solving change in internal energy of the system assumes no strategies for thermodynamics.
When the distance traveled, exert your own problem force.
Consider a car's gasoline engine.
A hand-driven tire pump has a 2.50- cm can.
The maximum stroke of 30.0 cm is one of the things to consider.
Take a car trip into the mountains.
In order to calculate the overall efficiency of the car for the trip, you have to do a problem.
Compare this efficiency to the efficiency quoted for gasoline engines and discuss why the efficiency is so much better.
Gain in altitude and speed, mass of the car, distance traveled, and typical fuel economy are some of the factors to consider.
A heat engine does 10 kJ of work and 8.25 kJ of 40.0%.
There is a gasoline engine that has an efficiency of 30.0%.
What is the maximum efficiency of a heat engine?
The steam locomotives have an efficiency of 17.0% and were upgraded, which resulted in an improvement in operate with a hot steam temperature.
Show how you follow the steps.
If you want to operate an ideal refrigerator with a heat transfer to the environment at and has a cold temperature of, you would like it to Carnot efficiency of 0.800.
The performance of the hot temperature is calculated by its coefficient of performance.
Unreasonable results heating an environment.
Suppose you have an ideal refrigerator that cools an conditioner or refrigerator that has heat transfer to British thermal units of heat transfer from a cold environment.
Explicitly show how you follow the steps in the Problem-Solving the Unavailability of Energy Strategies for Thermodynamics.
The large change in entropy means that the direct heat transfer energy has become unavailable to do work, which implies a large amount of does its cost compare with the direct heat transfer energy.
A hot rock ejected from a volcano's lava fountain cools with this heat transfer, assuming it operates between from to and has a constant temperature of 950 J/K.
In the Problem-Solving Strategies for Entropy, show how you follow the steps from its surface into dark empty space.
The deep space's effective temperature is not enough to do work.
Show how you follow the steps.
A large electrical power station produces 1000 MW of heads and 51 tails, 50 heads and 50 tails, and 51 heads electricity with an efficiency of 35.0%.
The tails count the number of heads and tails about twice a minute.
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