To solve this problem, we need to determine the change in the internal energy of the system using the first law of thermodynamics, which is given by the equation:
[tex]\[
\Delta U = Q - W
\][/tex]
where:
- [tex]\(\Delta U\)[/tex] is the change in the internal energy of the system,
- [tex]\(Q\)[/tex] is the heat exchanged by the system, and
- [tex]\(W\)[/tex] is the work done by the system.
Given the problem, we have:
- The system does 80 J of work on its surroundings, so [tex]\(W = 80 \text{ J}\)[/tex].
- The system releases 20 J of heat into its surroundings. Since the heat is released, [tex]\(Q\)[/tex] is negative, thus [tex]\(Q = -20 \text{ J}\)[/tex].
Now, we substitute the values of [tex]\(Q\)[/tex] and [tex]\(W\)[/tex] into the equation:
[tex]\[
\Delta U = -20 \text{ J} - 80 \text{ J}
\][/tex]
[tex]\[
\Delta U = -100 \text{ J}
\][/tex]
Therefore, the change in the internal energy of the system is [tex]\(-100\)[/tex] J.
The correct answer is:
[tex]\[
\boxed{-100 \text{ J}}
\][/tex]
