Why are there two different forms of the 1st law of thermodynamics?

[najma]

Homework Statement

Hi everyone, in 2 of my physics books the 1st law of thermodynamics is stated in 2 different ways:
I am unsure why these are stated in 2 different forms. Here is what I think:

Homework Equations

1. Eth=W+Q
2. Eth=Q-W

The Attempt at a Solution

2. takes into consideration the fact that when heat is added to a system then the system does work on the surroundings. for example in a cylinder filled with gas and covered with a piston: when heat is added (temperature increases therefore the internal energy also increases, this causes the piston to move up by dx and since there is a force exerted on the system (in the opposite direction dx) work becomes negative. hence, w=-pdV. therefore the first law becomes Q-W.
1. equation is a more general form the law and it doesn't take into consideration the sign of work.

Is this the right explanation?

 

[TSny]

Some texts use the symbol W to represent work done by the system on the environment. Other books define W as the work done on the system by the environment. These two ways of defining W will generally have the same magnitude but differ in sign.

 

[najma]

So I was partially right then! Thank you TSny!

 

[dipole]

It's a difference in the definition of work. The sign is negative when work is stated as "work done by the system" and the sign is positive when work represents "work done on the system".