The concepts of heat and temperature seem familiar to us.
The term heat refers to the transfer of thermal energy from one body to another.
An object can contain thermal energy due to the random motion of its molecule, but it doesn't contain heat because it isn't energy in transit.
The measure of an object's internal thermal energy is called temperature.
There are three modes in which energy can be transferred.
An iron skillet is sitting on a hot stove, and you accidentally touch the handle.
There is a transfer of thermal energy to your hand.
Conduction is the process by which this happens.
The atoms in the handle of the hot skillet cause them to vibrate more rapidly, heating up your hand.
If there is a temperature difference between the two objects, heat conducts from one point to another.
As the air around a candle flame warms, it expands, becomes less dense than the surrounding air, and thus rises.
In the case of air, heat is transferred away from the flame by the large scale motion of the fluid.
This is not static.
The sun's fusion reactions give rise to radiation that is transferred across millions of kilometers of empty space.
The absorption of the energy carried by the light waves is what defines heat transfer by radiation.
The atoms or molecule that make up a gas do not move around in fixed positions.
A confined gas exerts a force on the walls of its container because the molecule are zipping around inside the container.
The pressure, P, is the magnitude of the force per unit area.
The more pressure the gas molecule exerts, the faster they are moving.
Pressure, volume, and temperature are the three physical properties of a gas.
The universal gas constant is called K. The ideal gas law is an equation.
It can be written as NkBT, where Boltzmann's constant is 1.38 x 10 -23 J/K.
The ideal gas law shows how the variables are related to each other.
This is a bad assumption for a charged gas, where the individual charges would only interact weakly, but it is a good assumption for a neutral gas, where the atoms would only interact weakly.
For a fixed volume of gas, an increase in P gives a proportional increase in T. The pressure increases when the gas molecule strikes the walls of the container with more force.
We can find that the pressure exerted by N molecule of gas in a container of volume V is related to the average energy of the molecule by usingNewton's Second Law.
The ideal gas law has a value of nRT.
Since, by definition, N is nN A, we can rewrite this equation in the form of N A K avg.
The absolute temperature of the sample is directly proportional to the average translational kinetic energy of the gas molecule.
You must use kelvins as your temperature unit.
It's important to know that the molecule in the container has a wide range of speeds, some are slower than others.
The root-mean-square speed gives us an average speed that is easy to calculate from the temperature of the gas.
The temperature is a measure of energy.
If the temperature is given in kelvins, then it must quadruple since v rms is proportional to the square root of T.
The volume of the cylinder is 2 h, where the radius is and the height is.
The ideal gas law can be used to find P since we know V and T. The gas pressure times the area of the lid can be used to find the force on the lid.
This is about 1,600 pounds of force.
The bottom of the lid feels a pressure of 1.018 x 10 5 Pa that exerts a force upward, but the top of the lid feels a pressure of 1.013 x 10 5 Pa that exerts a force.
There are two ways in which energy can be transferred between a system and environment.
Work is when a force acts over a distance.
When energy is transferred due to a difference in temperature, it's called heat.
The study of the energy transfers involving work and heat, and the resulting changes in internal energy, temperature, volume, and pressure is called thermodynamics.
When two objects are brought into contact, heat will flow from the warmer object to the cooler one.
If objects 1 and 2 are in thermal equilibrium with each other, then objects 3 and 4 are also in thermal equilibrium with each other.
The first law of thermodynamics is a statement of how to conserve energy.
In any system of thermodynamics, energy is created and destroyed in the form of heat.
The prototype that's studied extensively in thermodynamics is the following example.
An insulated container filled with an ideal gas rests on a heat source that can act as a heat sink.
The container can be raised or lowered with the help of the weighted piston.
The system is composed of confined gas and surroundings.
Once the pressure, volume, and temperature of the gas are known, the equation that connects these state variables is the ideal gas law.
We'll imagine doing different experiments with the gas, such as heating it or allowing it to cool or increase or decrease the weight on the piston, and studying the energy transfers and the changes in the state variables.
The pressure and volume can be plotted on a diagram if the system and its surroundings are in thermal equilibrium.
We can study how the system is affected when it moves from one state to another by following the path of the P-V diagram.
When the volume of the gas changes, work is done by the system.
Imagine that the weight pushes the piston downward, causing a decrease in volume.
The pressure stays constant at P.
The circumstances under which work is defined to be positive or negative are different from textbook to textbook.
The negative signs we have included in the equations are similar to those used in the AP Physics 2 Exam.
When work is being done on the system, it is considered to be positive for the exam.
Energy is being added to the system because V is negative.
V is positive.
The work is negative in agreement with intuition that energy is leaving the system.
The pressure P doesn't change during the process.
If P does not change, the work is equal to the area under the curve in the P - V diagram; if the volume increases, the work is negative, but if the volume decreases, the work is positive.
When moving left to right or right to left, processes in P-V diagrams are drawn with arrows to indicate which direction the process goes.
The process is taken from an initial state with a particular P and V value to a final state where P and V have changed.
Work is only done along path 2 if the gas is brought from state a to state b.
The volume of the gas doesn't change from d to b, so no work can be done.
The amount of work done by a gas depends on the path between the initial and final states of the system.
Different paths give different values.
Experiments show that the value of Q + W is not path dependent, and that it describes a change in a fundamental property.
Q + W is equal to U.
This is the case regardless of the process that brought the system to its final state.
The interpretation of work is explained in the statement of the First Law.
The First Law states that W and Q are separate physical mechanisms that can add or subtract energy from the system.
The gas did negative work against it's surroundings.
The process is called isobaric if the pressure remains constant.
The path of the gas is different than the initial and final states.
No work is done over paths 1 and 3 because the volume doesn't change.
The expanding gas does negative work against it's surroundings.
It must be the same.
U is 4,500 J.
An isochoric process is one that does not change in volume.
An isochoric process is illustrated by a vertical line in a P - V diagram and, since no change in volume occurs, W is 0.
The heat transferred causes the change in internal energy.
U is not positive.
It is said that a process such as this, which begins and ends at the same state, is a cycle.
W is the total amount of work done.
Overall, work was done on the gas by the surroundings if W is positive.
The total work done is equal to the area enclosed by the loop, with clockwise and counterclockwise travel taken as negative and positive.
It's true that Q is -2,000 J, which is always the case for a cyclical process.
It is said that a process with no variation in temperature is isothermal.
If the temperature remains constant, a process is isothermal.
The temperature is determined by the internal energy of the gas, which is affected by changes in Q, W, or both.
Even if Q is not 0, it is possible for U to remain the same.
This is the key to the problem.
Since T doesn't change from a to d, neither can the internal energy, which depends entirely on T. It must be true that Qad is -Wad.
Qad must be at least -1,650 J.
As the gas expands, it uses all of the energy it absorbed to do negative work, pushing the piston upward.
Two pure gases are separated by a partition.
The gases would mix and the positions of the gas molecule would be random.
A closed system that shows a high degree of order tends to evolve in such a way that its degree of order decreases.
In other words, disorder increases.
The term "disorder" makes the concept sound negative.
Increasing molecular freedom is what entropy is described as.
The reason why broken glass doesn't put itself back together is because of this.
If we started with the box on the right, containing the mixture of the gases, it would be almost impossible for the molecule of Gas 1 to move to the left side of the box at the same time as the molecule of Gas 2 did.
If we were to watch a movie of this process, and saw the mixed-up molecules suddenly separate and move to opposite sides of the box, we would assume that the film was running backwards.
The direction of time is defined by the second law of thermodynamics.
Time flows in such a way that ordered systems become disorganized.
Disordered states don't spontaneously become ordered without any other changes.
The total amount of disorder will never decrease.
It is possible for the system's entropy to decrease, but it will always be at the expense of the surroundings.
Water's entropy decreases when it's cold.
The ice crystal has a more structured order than the random water molecule in the liquid phase, so the water's entropy decreases when it is frozen.
When water is frozen, it creates disorder in the surroundings.
If we were to figure out the total change in the water's entropy, we would find that it was more than compensated for by the increase in the surroundings.
The second law of thermodynamics increased the total entropy of the system and its surroundings.
The second law has similar statements.
The second law of thermodynamics says that heat always flows from an object at higher temperature to an object at lower temperature, never the other way around.
The heat always flows from hot to cold.
It is impossible for a heat engine to operate at 100% efficiency, or equivalently, that it is impossible to convert heat into work, according to another form.
Over time, an isolated system does not decrease in entropy.
Over time, a non-idealized isolated system increases in entropy.
The form of heat that is given off is called the entropy.
If the surroundings to the system increase in entropy than the decrease in the system, it is possible for the system's entropy to decrease.
As real world systems transfer heat and work, the entropy of the universe will increase over time.
The second law of thermodynamics deals with heat engines.
It is easy to convert work to heat by rubbing your hands together.
A heat engine is a device that uses heat.
An example is the internal-combustion engine in a car.
We're only interested in engines that take their working substance through a cycle so that it can be repeated.
The basic components of a heat engine are simple: Energy in the form of heat comes into the engine from a high-temperature source, some of this energy is converted into useful work, the rest is ejected as exhaust heat into a low-temperature sink, and the system returns to its original
It is necessary for U to be 0.
The net heat absorbed by the system is the same as the work done by the system.
The heat that is absorbed from the high- temperature source is referred to as Q H, and the heat that is discharged into the low- temperature source is referred to as Q C. The net heat absorbed is Q H + Q C because heat coming in is positive and heat going out is negative.
To show that Q net is less than Q H, it's customary to write it as Q H - Q C.
All engines work to convert heat into work by exchanging energy from a reservoir at higher temperature to a lower one.
A good example of this is a fridge.
Liquid moves through tubes in a fridge to remove heat from the inside of the fridge.
The sensation of low heat content is what cold is about.
The back of the fridge feels hot.
Exhaust heat is always produced for any heat engine.
It is not possible to convert heat into useful work.
A heat engine draws 800 J of heat from its high- temperature source and discards 450 J of exhaust heat into its cold- temperature reservoir during each cycle.
Chapter 12 contains solutions.
A container holds a mixture of two gases.
The average energy of a CO 2 molecule and an H 2 molecule is measured by K C and K H.
The ideal gas is compressed from 20 m 3 to 10 m 3.
5 J of work is done to compress the gas.
An ideal gas can be found in a container with a fixed volume.
The amount of gas is slowly increasing.
The experiment is done in a way that keeps the temperature constant.
The data is collected.
The internal energy of a sample of confined gas is increased through a series of processes.
The isothermal expansion of the gas occurs in one of the steps of the Carnot cycle.
A cup of coffee is sealed inside a container.
A long time can go on.
The coffee has caused an increase in the box's entropy.
70 J of heat flows into the system when a system is taken from state a to state b along the path shown in the figure below.
Qgained + Qlost are the numbers in an isolated system.
The cross-sectional area, the temperature difference between the two sides, and the thickness between the two ends are all related to the rate at which heat is transferred.
Pressure is the result of the molecule colliding with one another and with the sides of the container.
The force per unit area on the walls of the container is known as the ideal gas law.
The particles in the gas are moving with a large distribution of different speeds, but this is related to the most likely speed a particle will be moving.
Under a pressure- vs-volume graph, the work can be found.
If there is a change in volume, the equation W is used to calculate the work.
Work is done on the system by the surroundings if W positive is true.
Work is done by the system on the surroundings if there is a negative W. A flow of heat from the higher temperature surroundings to the lower temperature system is called a Q positive.
The idea that a heat engine is to produce positive work is consistent with this.
The First Law must be written as U + W + Q, and W must be interpreted differently from Q.
When heat is added to the system, Q is still positive, but W is positive when work is done by the system on the surroundings, decreasing the internal energy of the system.