Finally Understand Signs of U, Heat, and Work

A few weeks ago, I published a blog regarding the sign of work, which can be seen in here: http://understandhowthingworks.blogspot.com/2014/06/understand-sign-of-work.html

Today, I would like to wrap up all of the confusions regarding the sign.

Some of the notes are taken from LINK. Much thanks to their helpful illustrations and notes.

Let's begin with our universal first law of thermodynamic. U=Q+W

Sign of Q: 

When Q is positive, Heat is taken into the system, increasing the temperature, increasing the internal energy (U) which becomes positive.

When Q is negative, Heat is taken away from the system, decreasing the temperature, decreasing the internal energy U which becomes negative.

Sign of W:

When W is positive, the surrounding does work on the system, increasing the internal energy U which becomes positive. This means that temperature of the system will also increase because internal energy U is directly related to temperature.

This is the so-called Work is being done on the system (by the surrounding--to make it clear). This process is called Compression. As a result, the equation becomes U= E+W (Note: you can think of it as you need positive work to increase the internal energy U, that's why W HAS to be positive).

When W is negative, the system is doing work to the surrounding, decreasing the internal energy U which becomes negative. As a result, temperature of the system also decreases.

This is the so-called Work is being done by the system. This process is called expansion. As a result, the equation becomes U= E-W (Note: you can also think of this as you need work to be negative to decrease the internal energy U).

These observations explain why gas cools when expands and gas heats up when being compressed.

I hope this blog post has cleared out any confusion that any student might have had in their school.

Understand the sign of work in electricity

Imagine the plates of a capacitor has a potential difference of 10V. How much work must be done in order to move the electron from the negative plate to positive plate?

Given that electric field goes from positive plate to negative plate. If you want to move the electron from negative to positive plate, you need to invest some energy to make that happen (positive work) because you are going up against the electric field.

The equation to solve that is W= qV. I was very confused about the sign of work due to the sign of V and q. However, I realize that no matter what you do, your work must be POSITIVE! Therefore, you can do whatever you want to q and V to make work positive :)

Understand the sign of work

At some point, we are all confused by the meaning of the sign of work; at least I did. 

Here is how I interpret the sign of work.

We all know that W=P times change of V.

Let's think of a situation in the perspective of a system (cylinder with a piston on top of it).

When the final volume is less than the initial volume, we have negative work. What does this mean?

It means that the system is not doing work! It is not investing any energy (negative work). So, work is being done on the system!

What if final volume is greater? that means the system is doing work! The system is investing energy to do work (positive). We describe this as work is being done by the system!