Question

1. A scientist very carefully does mechanical work on a container of liquid sodium. The liquid sodium loses 300 J of energy to its surroundings but gains 250 J of energy overall. How much work did the scientist do?

Answer 1

The work that is done by the scientist is equal to the sum of lost energy and gained energy, because

$U_{fin} - U_{init} = -Q_{lost} + A,$ so $250\,\mathrm{J} = -300\,\mathrm{J} + A,$ therefore $A=550\,\mathrm{J}.$ So the work that was done by scientist on the system is positive.