Talk:First Law of Thermodynamics
The differentials for heat and work need to be changed to inexact differentials
- Explain the differentials. Karajou (talk) 12:28, 20 November 2016 (EST)
- The internal energy is an exact differential as internal energy is a function of state. That is to say that how it changes is independent of the path taken between two states.
- Heat and work are inexact differentials as they do depend on the paths taken.
- Consider this diagram http://www.antonine-education.co.uk/Image_library/Physics_5_Options/Applied_Physics/App_04/Cycle_1.gif
- The work done on the gas is proportional the area under the path taken. You can see that going from b to c directly more work is done that if we go from b to a to d to c.
- Basically, for heat and work, the need to be changed to
- I'm guessing you are talking about changing the sign of the work term from to . The sign of and depends on how you define those terms and is arbitrary. If we define as the work the system does on its surroundings, then the first law is:
- If instead we define it as the work done on the system it is:
- The magnitude of the work done is the same in both cases but the sign is different because we have defined it differently. Different textbooks use different conventions, but so long as you are consistent with your definitions of the terms, it doesn't matter and you will end up with the same answer to any problem.
- I learnt the first law as , so when I added it to the Thermodynamics page, that was the form I used. When I saw this page I edited it to change the differentials to be inexact for heat and work, and then to be consistent, changed the definition of work and its sign in the equation.
- If you want you can change the Thermodynamics page to have the definition that was on here previously.
- These are some sites that explain it. They use different conventions for the sign of work: , 
- The first explains what exact/inexact differentials are and the second shows an example of someone defining in the way I would. Note that inexact differentials are often denoted by a or using a bar (I don't know the Latex for that)
- Hope it helps PeterIceHockey (talk) 14:57, 20 November 2016 (EST)