# Thermodynamics

## The First Law of Thermodynamics and Some Simple Processes


### Learning Objectives

By the end of this section, you will be able to:
1. Describe the processes of a simple heat engine.
2. Explain the differences among the simple thermodynamic processes—isobaric, isochoric, isothermal, and adiabatic.
3. Calculate total work done in a cyclical thermodynamic process.
One of the most important things we can do with heat transfer is to use it to do work for us. Such a device is called a heat engine. Car engines and steam turbines that generate electricity are examples of heat engines.  shows schematically how the first law of thermodynamics applies to the typical heat engine.
The illustrations above show one of the ways in which heat transfer does work. Fuel combustion produces heat transfer to a gas in a cylinder, increasing the pressure of the gas and thereby the force it exerts on a movable piston. The gas does work on the outside world, as this force moves the piston through some distance. Heat transfer to the gas cylinder results in work being done. To repeat this process, the piston needs to be returned to its starting point. Heat transfer now occurs from the gas to the surroundings so that its pressure decreases, and a force is exerted by the surroundings to push the piston back through some distance. Variations of this process are employed daily in hundreds of millions of heat engines. We will examine heat engines in detail in the next section. In this section, we consider some of the simpler underlying processes on which heat engines are based.

### PV  Diagrams and their Relationship to Work Done on or by a Gas

A process by which a gas does work on a piston at constant pressure is called an isobaric process. Since the pressure is constant, the force exerted is constant and the work done is given as
See the symbols as shown in . Now , and so
Because the volume of a cylinder is its cross-sectional area  times its length , we see that , the change in volume; thus,
Note that if  is positive, then  is positive, meaning that work is done by the gas on the outside world.
(Note that the pressure involved in this work that we’ve called    
    
      is the pressure of the gas inside the tank.  If we call the pressure outside the tank     
    
     , an expanding gas would be working against the external pressure; the work done would therefore be    
    
       (isobaric process). Many texts use this definition of work, and not the definition based on internal pressure, as the basis of the First Law of Thermodynamics.  This definition reverses the sign conventions for work, and results in a statement of the first law that becomes  
    
     .)
It is not surprising that , since we have already noted in our treatment of fluids that pressure is a type of potential energy per unit volume and that pressure in fact has units of energy divided by volume. We also noted in our discussion of the ideal gas law that  has units of energy. In this case, some of the energy associated with pressure becomes work.
 shows a graph of pressure versus volume (that is, a  diagram for an isobaric process. You can see in the figure that the work done is the area under the graph. This property of  diagrams is very useful and broadly applicable: the work done on or by a system in going from one state to another equals the area under the curve on a .
We can see where this leads by considering (a), which shows a more general process in which both pressure and volume change. The area under the curve is closely approximated by dividing it into strips, each having an average constant pressure . The work done is  for each strip, and the total work done is the sum of the . Thus the total work done is the total area under the curve. If the path is reversed, as in (b), then work is done on the system. The area under the curve in that case is negative, because  is negative.
 diagrams clearly illustrate that the work done depends on the path taken and not just the endpoints. This path dependence is seen in (a), where more work is done in going from A to C by the path via point B than by the path via point D. The vertical paths, where volume is constant, are called isochoric processes. Since volume is constant, , and no work is done in an isochoric process. Now, if the system follows the cyclical path ABCDA, as in (b), then the total work done is the area inside the loop. The negative area below path CD subtracts, leaving only the area inside the rectangle. In fact, the work done in any cyclical process (one that returns to its starting point) is the area inside the loop it forms on a  diagram, as (c) illustrates for a general cyclical process. Note that the loop must be traversed in the clockwise direction for work to be positive—that is, for there to be a net work output.

### Reversible Processes

Both isothermal and adiabatic processes such as shown in  are reversible in principle. A reversible process is one in which both the system and its environment can return to exactly the states they were in by following the reverse path. The reverse isothermal and adiabatic paths are BA and CA, respectively. Real macroscopic processes are never exactly reversible. In the previous examples, our system is a gas (like that in ), and its environment is the piston, cylinder, and the rest of the universe. If there are any energy-dissipating mechanisms, such as friction or turbulence, then heat transfer to the environment occurs for either direction of the piston. So, for example, if the path BA is followed and there is friction, then the gas will be returned to its original state but the environment will not—it will have been heated in both directions. Reversibility requires the direction of heat transfer to reverse for the reverse path. Since dissipative mechanisms cannot be completely eliminated, real processes cannot be reversible.
There must be reasons that real macroscopic processes cannot be reversible. We can imagine them going in reverse. For example, heat transfer occurs spontaneously from hot to cold and never spontaneously the reverse. Yet it would not violate the first law of thermodynamics for this to happen. In fact, all spontaneous processes, such as bubbles bursting, never go in reverse. There is a second thermodynamic law that forbids them from going in reverse. When we study this law, we will learn something about nature and also find that such a law limits the efficiency of heat engines. We will find that heat engines with the greatest possible theoretical efficiency would have to use reversible processes, and even they cannot convert all heat transfer into doing work.  summarizes the simpler thermodynamic processes and their definitions.

### Test Prep for AP Courses


### Section Summary

1. One of the important implications of the first law of thermodynamics is that machines can be harnessed to do work that humans previously did by hand or by external energy supplies such as running water or the heat of the Sun. A machine that uses heat transfer to do work is known as a heat engine.
2. There are several simple processes, used by heat engines, that flow from the first law of thermodynamics. Among them are the isobaric, isochoric, isothermal and adiabatic processes.
3. These processes differ from one another based on how they affect pressure, volume, temperature, and heat transfer.
4. If the work done is performed on the outside environment, work () will be a positive value. If the work done is done to the heat engine system, work () will be a negative value.
5. Some thermodynamic processes, including isothermal and adiabatic processes, are reversible in theory; that is, both the thermodynamic system and the environment can be returned to their initial states. However, because of loss of energy owing to the second law of thermodynamics, complete reversibility does not work in practice.

### Conceptual Questions


### Problem Exercises
