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.