First law of thermodynamics

Question

I have sometimes seen the first law defined as :

DU = q - w

While in some books and texts I have seen it to be defined as :

DU = q + w

I would like to know that which definition is correct and why?

Answer 1

It is a matter of convention in the definition of the work W.

• If you define work done as positive when it is done onto (= given to) the fluid, then the equation is U = Q + W because internal energy increases with heat input and work received.
• If on the other hand you define work done as positive when it is done by (= taken away from) the fluid, then the equation is U = Q - W because internal energy increases with heat input and decreases with work done.