The first law of Thermodynamics is $$ dU = dQ – dW $$ Halliday and Resnick says that energy transfer of heat Q $\text{occurs to the system}$ (which is by convention positive) and a Work W is done $\text{by the system}$ (which is by convention again is positive). this total energy transfer is the internal energy so shouldn't internal energy U be defined Q + W rather than Q – W.
Please let me know why is it defined Q – W whereas in chemistry it is defined as Q + W?
The above conventions are mentioned in Halliday Resnick
Best Answer
The convention for the International Union of Pure and Applied Chemistry (IUPAC) is the Kelvin form
$dU = \delta q + \delta w$
Heat eXits the system in an eXothermic process (and eNters in an eNdothermic process). Work eXits the system when it is done by the system. In either case (heat or work), exiting values are negative.
The convention for engineering is the Clausius form (which was the first statement of the first law)
$dU = \delta q - \delta w$
The same conventions apply for heat (negative for exothermic processes, positive for endothermic processes). For engineers, work done by the system has utility for us and is given a positive sign.
Both forms are explained here