To determine the change in internal energy of a system, we use the formula:
[tex]\[ \Delta U = Q - W \][/tex]
where:
- [tex]\(\Delta U\)[/tex] is the change in internal energy,
- [tex]\(Q\)[/tex] is the heat added to the system, and
- [tex]\(W\)[/tex] is the work done by the system.
In this problem, we have:
- 60 J of heat is released from the system (since it is released, [tex]\(Q\)[/tex] is negative), so [tex]\(Q = -60\)[/tex] J.
- 30 J of work is done on the system (since work is done on the system, [tex]\(W\)[/tex] is also negative), so [tex]\(W = -30\)[/tex] J.
Substituting these values into the formula:
[tex]\[ \Delta U = -60 - (-30) \][/tex]
Solving this step-by-step:
[tex]\[ \Delta U = -60 + 30 \][/tex]
[tex]\[ \Delta U = -30 \][/tex]
Therefore, the change in internal energy is [tex]\(-30\)[/tex] J.
The correct answer is [tex]\(\boxed{-30 \text{ J}}\)[/tex].
