The Second Law of Thermodynamics

Introduction

Outline

• The Second Law
  • Definitions of terms
  • Heat Pumps and Refrigerators
• Practice with the Concepts
• Discussion Points

The Second Law

Conservation of Energy Forms

The second law has several different forms.

• Clausius: not all processes are reversible; heat flows naturally from hot to cold object; heat will not flow spontaneous from cold to hot object.
• Kelvin-Plank: no device can convert heat energy completely into mechanical work.
• General statement: the disorder (entropy) of the universe increases with an energy conversion

These observations have practical ramifications for any system which tries to effect a heat exchange from one area and temperature to another.

Heat engines work by converting heat to mechanical work. Heat is pumped into the system, some work is done, and some heat exits the system (at a lower temperature). The thermal efficiency of the engine is measured as a ration of the work done to the heat which is put into the system: $$e=\frac{W}{Q_{\mathrm{in}}}$$

Because Q_in occurs at a higher temperature than Q_out, so thermal efficiency is sometimes written as $$e=\frac{W}{Q_H}$$

Now, because of conservation of energy, $$Q_{\mathrm{in}}=W+Q_{\mathrm{out}}\Rightarrow Q_H=W+Q_L$$ so we can do some substitutions if we need to, depending on the information we are given or can measure about a specific system.

Practice with the Concepts

Heat Pumps and Refrigerators

Heat pumps transfer energy from low temperature reservoirs to high temperature on. Many heat pumps can be reversed to move heat to cold regions as well.

Instead of rating pumps by thermal efficiency, we rate them by a coefficient of performance, or COP, depending on the direction of the flow.

Refrigerators or air conditions have $$\mathrm{COP}=\frac{Q_{\mathrm{in}}}{W}=\frac{Q_L}{W}=\frac{Q_L}{Q_H-Q_L}$$

Heaters have $$\mathrm{COP}=\frac{Q_{\mathrm{out}}}{W}=\frac{Q_H}{W}=\frac{Q_H}{Q_H-Q_L}$$

Notice that the efficiencies are not the same: in general, heaters will be more efficient that refrigerators. That's because heat flow from cold to hot regions (which is what refrigerators accomplish) takes work --it runs against the natural direction of entropy.

But what if you could have a refrigerator work with 100% efficiency? Sadi Carnot theorized that such an engine would have to operate infinitely slowly, and so is impossible. Nevertheless, Carnot's idealized engine is useful because it allows us to determine the limits of operation for a particular situation. Since no work would be done, the amount of heat flow would be directly related to the temperature changes.

The efficiency of the ideal engine $$e=\frac{T_H-T_L}{T_H}=1-\frac{T_L}{T_H}$$ (using the same kind of algebraic manipulations we did above). Temperatures are much more easily measured than abstract heat flows (remember that we had to measure temperature and calculate heat flow for our calorimeters). This relationship gives us another way of dealing with heat flows in engine and pump systems.

Discussion Points

• Can you warm a kitchen in winter by leaving the oven door open? Can you cool the kitchen on a hot summer day by leaving the refrigerator door open? Explain.
• The COPs are defined differently for heat pumps and air conditioners. Explain why.

---

© 2005 - 2025 This course is offered through Scholars Online, a non-profit organization supporting classical Christian education through online courses. Permission to copy course content (lessons and labs) for personal study is granted to students currently or formerly enrolled in the course through Scholars Online. Reproduction for any other purpose, without the express written consent of the author, is prohibited.