Chapter 3. The First Law of Thermodynamics
3.3 First Law of Thermodynamics
Learning Objectives
By the end of this section, you will be able to:
- State the first law of thermodynamics and explain how it is applied
- Explain how heat transfer, work done, and internal energy change are related in any thermodynamic process
Now that we have seen how to calculate internal energy, heat, and work done for a thermodynamic system undergoing change during some process, we can see how these quantities interact to affect the amount of change that can occur. This interaction is given by the first law of thermodynamics. His humorous statement of the first law of thermodynamics is stated “you can’t win,” or in other words, you cannot get more energy out of a system than you put into it. We will see in this chapter how internal energy, heat, and work all play a role in the first law of thermodynamics.
Suppose Q represents the heat exchanged between a system and the environment, and W is the work done by or on the system. The first law states that the change in internal energy of that system is given by [latex]Q-W[/latex]. Since added heat increases the internal energy of a system, Q is positive when it is added to the system and negative when it is removed from the system.
When a gas expands, it does work and its internal energy decreases. Thus, W is positive when work is done by the system and negative when work is done on the system. This sign convention is summarized in Table 3.1. The first law of thermodynamics is stated as follows:
First Law of Thermodynamics
Associated with every equilibrium state of a system is its internal energy [latex]{E}_{\text{int}}.[/latex] The change in [latex]{E}_{\text{int}}[/latex] for any transition between two equilibrium states is
where Q and W represent, respectively, the heat exchanged by the system and the work done by or on the system.
| Thermodynamic Sign Conventions for Heat and Work | |
|---|---|
| Process | Convention |
| Heat added to system | [latex]Q>0[/latex] |
| Heat removed from system | [latex]Q < 0[/latex] |
| Work done by system | [latex]W>0[/latex] |
| Work done on system | [latex]W < 0[/latex] |
The first law is a statement of energy conservation. It tells us that a system can exchange energy with its surroundings by the transmission of heat and by the performance of work. The net energy exchanged is then equal to the change in the total mechanical energy of the molecules of the system (i.e., the system’s internal energy). Thus, if a system is isolated, its internal energy must remain constant.
Although Q and W both depend on the thermodynamic path taken between two equilibrium states, their difference [latex]Q-W[/latex] does not. Figure 3.7 shows the pV diagram of a system that is making the transition from A to B repeatedly along different thermodynamic paths. Along path 1, the system absorbs heat [latex]{Q}_{1}[/latex] and does work [latex]{W}_{1};[/latex] along path 2, it absorbs heat [latex]{Q}_{2}[/l