Systems and Sign Conventions

Table of Contents
Thermodynamics Gateway Page
In this module:
Kinetic and Potential Energy
The First Law of Thermodynamics
Systems and Sign Conventions

Throughout the Thermodynamics Tutorial you will be shown and taught a method for working thermodynamics problems. Following this method closely will increase your chances of successfully solving the problem, especially in the beginning when the terms, concepts, and calculations may be unfamiliar to you.

The first two steps to follow in solving a thermodynamics problem are:

1. Define the system and the surroundings. The system is some object or collection of objects that the problem focuses on, usually one that acts most or causes the most change in the problem, while the surroundings are anything else capable of interacting with (exchanging energy with) the system.

2. Identify and assign signs (positive or negative) to all the kinds of energy and work that enter or leave the system.

In a complicated problem, you may have to repeat these steps more than once, but for now you should only have to do them once.

Let's look at the circus act from the previous page again. Since it is the elephant, and especially its front legs, that cause most of the action in the problem, let's define the front half of the elephant as the system. Everything else, especially the rest of the elephant and the circus performer, are the surroundings. Now, let's take a look at what happens in each step.

Click on the step numbers below to see the circus act again from the perspective of the system and its surroundings. Click on the mouse icon at left to clear the images and text.

The system has zero potential energy.
A quantity of energy is transferred to the system from the surroundings (the muscles of the elephant), increasing the potential energy of the system.
The potential energy is converted to kinetic energy, but no energy leaves the system.
The system does work on its surroundings (the performer), causing motion against the force of gravity.
The system has zero potential energy.

Now we are ready for step 2 of the thermodynamics problem-solving process. Energy and work (remember, they are the same thing) enter or leave the system at two points: when the elephant's muscles increase the potential energy of its legs and when it does work to propel the performer into the air. The General Rule for assigning signs is this:

If energy enters the system, its sign is positive.
If energy leaves the system, its sign is negative.
If work is done on the system, its sign is positive.
If work is done by the system, its sign is negative.

Thus, the energy entering the elephant's front legs has a positive sign. The work the elephant does on the performer has a negative sign.

Systems and Sign Conventions