Asystem absorbed 44 joules of heat from its surroundings. after doing work, the increase in the internal energy of the system is 32 joules. how much energy was used by the system to do useful work?

We can solve the problem by using the first law of thermodynamics:

where
is the variation of internal energy of the system
Q is the heat absorbed by the system
W is the work done by the system

In this problem, the heat absorbed by the system is Q=+44 J, and the increase in internal energy is . So we can rearrange the equation to calculate the work done:

and the work is positive, which means that it is done by the system on the surrounding.