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# Thermodynamics Study Guide (page 3)

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Updated on Sep 27, 2011

## First Law of Thermodynamics

As one defines the parameters in mechanics that characterize the mechanical state, position, and speed, then the interactions (force and torque) and the energies, we will similarly define parameters for the next concept. We have introduced the thermodynamic parameters previously (pressure, volume, temperature, and moles). We have talked about heat and internal energy exchange between systems. Now it is time to apply the principle of conservation of energy to this subject. The statement of the first law of thermodynamics does exactly this.

Any change in the system is due to exchange of energy with its surroundings. Energy is not a vector quantity, and therefore, we need a convention to establish the sign of these energies because of the different consequences of exchanging energy. For confirmation of this need, read ahead to the next example. At the beginning of this lesson, we talked about the convention for work; now it is time to define a convention for heat.

### First Law of Thermodynamics

The first law of thermodynamics, also called conservation of energy, says that the internal energy of a system changes from an initial value Ui to a final value Uf, due to heat exchange Q and work performed on or by the system, W.

ΔU = Uf – Ui = Q + W

Convention for Work
• Work is a positive quantity when work is performed on the system.
• Work is a negative quantity when work is performed by the system.

#### Example

You have two completely identical containers, and the same quantity of liquid is in both of them. You put one of them in contact with a colder object and it loses 100 J of heat. The other one you put in contact with a warm source and it gains 100 J. The energy is the same. Is the final state of the two containers the same?

#### Solution

The state is not similar because the system absorbing heat will have atoms and molecules moving faster: It has larger temperature, while the system that cools down will have slower particles and smaller temperature. Because the thermodynamic state is characterized by P, V, T, and m, even if the rest of the parameters are the same, the temperature is different, so the states are different.

## Second Law of Thermodynamics

The second and final law of thermodynamics refers to a "natural" process—the flow of heat. Numerous circumstances in your life have allowed you to experience the essence of this law.

There are other ways to express the meaning of this law. These other expressions require the introduction of machines, such as engines and refrigerators, or concepts, such as entropy. The formulation of these expressions varies with the field of study. So don't be surprised if you open a book geared toward engineering professionals and find the law expressed with engines or if you open a more advanced textbook and find a discussion about entropy. Each and every field of study introduces the law based on previous knowledge of that field of study.

### Second Law of Thermodynamics

Heat flows from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction.

## Simple Thermodynamic Processes

In nature, rarely is there complete and self-sustained thermal isolation of a system. That means that in most cases, the states of a system have at least one variable parameter, if not more. We will consider simple thermodynamic processes where all but one parameter vary.

Isobar process: This is a process in which pressure is constant (P = constant). In the section on thermodynamic work, we studied an isobar process and its PV-diagram, and we were able to find a simple way to calculate work from a geometrical interpretation. The work in such a process is the area under the PV-diagram.

Isochoric process or isoyolumic process: This is a process in which the volume is constant while the pressure varies, as in Figure 12.5.

At a constant volume:

ΔV = 0

W = – P · ΔV = 0 J

ΔU = Q + W = Q

The internal energy increases (ΔU > 0) if the system absorbs heat, and it decreases (ΔU < 0) if the system loses heat. As you can see in the figure, there is no area under the PV-curve, so there is no work.

Isothermal process: This is the process in which the temperature is constant. For an ideal gas, internal energy can be shown to be proportional with the temperature, hence in this process:

T = constant

ΔU = 0 J

ΔU = Q + W = 0

Q = – W

We interpret this expression as follows: If a system evolves without changing its internal energy, work will be done by the system only if it receives heat, and heat will be released by the system only if work will be done on it.

Adiabatic process: This is a process where no exchange of heat happens. When there is no heat exchange with the surroundings (thermal isolated system), the work can be done only at the expense of the changing internal energy.

If you compare the PV-diagram of the adiabatic and isothermal processes, you might mistakenly consider them identical. Although both of them are curves, in a PV-diagram, the slope of the adiabatic transformation is steeper than the slope of the isotherm at the same volume, as shown in Figure 12.6.

The two isothermals, shown by the symbol in the graph, intersect the adiabatic curve (Δ) evolving between T1 and T2 temperatures and the same volumes V1 and V2.

Let's study the first law:

Q = O J

ΔU= W = –P · ΔV

If the system expands, then the work is negative and the change in internal energy is negative also. This means the energy of the constituent particles and the temperature of the system decreases.

Based on these processes, machines such as heat engines and refrigerators have been constructed. A heat engine is a device that converts internal energy into work by heat flow from a high temperature source to a low temperature source. Because these machines have to go through multiple repetitions of the same process, we call the sequence of process a thermodynamic cycle. A refrigerator uses mechanical work to take heat from a cold source and release it to a hot source, effectively lowering the temperature of a system.

Practice problems of this concept can be found at: Thermodynamics Practice Questions

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