Why are the values for work done on isothermal and adiabatic compression negative?

Answer 1

Don't know but I believe the following is consistent with the history and development of thermodynamics. Thermodynamics first tackled analysis of a "heat engine" which, at the time, essentially meant a steam engine. By convention, an engine produced a work output which logically was positive (it would be poor marketing to sell a negative 1000 kw engine). The fuel used was positive - more acurately, the fuel produced by burning the fuel put positive heat into the engine. Again, by convention, heat in is positive and work out is positive. Note that heat coming out would be heat taken away ... subtracting heat or negative heat. So why does compressing a gas involve negative work? Gas expansion is the basic positive work producing process for heat engines and, since 1) compression is the opposite of expansion and 2) the total work needed to reversibly compress and expand a gas (back to the initial condition) is zero, then Work compression + Workexpansion = 0 so they better have opposite signs. The idea of work in and work out is closely tied to the idea of control volume. TSM