# 15.3 Introduction to the second law of thermodynamics: heat engines  (Page 5/10)

 Page 5 / 10

The net work done by a cyclical process is the area inside the closed path on a $\text{PV}$ diagram, such as that inside path ABCDA in [link] . Note that in every imaginable cyclical process, it is absolutely necessary for heat transfer from the system to occur in order to get a net work output. In the Otto cycle, heat transfer occurs along path DA. If no heat transfer occurs, then the return path is the same, and the net work output is zero. The lower the temperature on the path AB, the less work has to be done to compress the gas. The area inside the closed path is then greater, and so the engine does more work and is thus more efficient. Similarly, the higher the temperature along path CD, the more work output there is. (See [link] .) So efficiency is related to the temperatures of the hot and cold reservoirs. In the next section, we shall see what the absolute limit to the efficiency of a heat engine is, and how it is related to temperature.

## Section summary

• The two expressions of the second law of thermodynamics are: (i) Heat transfer occurs spontaneously from higher- to lower-temperature bodies but never spontaneously in the reverse direction; and (ii) It is impossible in any system for heat transfer from a reservoir to completely convert to work in a cyclical process in which the system returns to its initial state.
• Irreversible processes depend on path and do not return to their original state. Cyclical processes are processes that return to their original state at the end of every cycle.
• In a cyclical process, such as a heat engine, the net work done by the system equals the net heat transfer into the system, or $W={Q}_{\text{h}}–{Q}_{\text{c}}\phantom{\rule{0.25em}{0ex}}$ , where ${Q}_{\text{h}}$ is the heat transfer from the hot object (hot reservoir), and ${Q}_{\text{c}}$ is the heat transfer into the cold object (cold reservoir).
• Efficiency can be expressed as $\text{Eff}=\frac{W}{{Q}_{\text{h}}}$ , the ratio of work output divided by the amount of energy input.
• The four-stroke gasoline engine is often explained in terms of the Otto cycle, which is a repeating sequence of processes that convert heat into work.

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