Skill 8 of 14
In Progress

Sign conventions

Which of these is the correct energy conservation law:1

$$\unicode{x24b6} \quad E_1+Q+W=E_2\qquad\qquad\unicode{x24b7} \quad E_1-Q+W=E_2$$
$$\unicode{x24b8} \quad E_1+Q-W=E_2\qquad\qquad \unicode{x24b9} \quad E_1-Q-W=E_2$$

The answer is…

they all are! Or, they all might be.

Do you remember Newton’s 2nd law where forces were summed up? Do you remember how we couldn’t know which forces to give which sign before first having chosen a direction to mean ‘positive’?2 It seems we have a similar issue here with energies.

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  2. Thermal Physics’ (book), Michael Sprackling, The American Institute of Physics, vol. 1 of the Macmillan Physical Science series, 1991, (accessed Jun. 28th, 2020), ISBN 0-88313-919-4, chapter 4.5, pages 32-33
  3. Reasoning in Physics, The Part of Common Sense’ (book), Laurence Viennot, Kluwer Academic Publishers, 2001, (accessed Jun. 28th, 2020), ISBN 1-4020-0274-2, chapter 6
  4. Quantities, Units and Symbols in Physical Chemistry’ (article), E. R. Cohen, T. Cvitas, J. G. Frey and others, IUPAC & RSC Publishing, IUPAC (International Union of Pure and Applied Chemistry) Green Book, 3rd ed., 2nd printing, 2008, (accessed Jun. 28th, 2020), ISBN 978-0-85404-433-7
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  8. Why are the sign conventions of work done in thermodynamics different for physics and chemistry?’ (web page, forum conversation), Sounak Sinha, Vijeet Shivappa, Jaydeep Deshpande and others, Quora, 2015-2019, (accessed Jul. 28th, 2020)