What is the change in internal energy if 60 J of heat is released from a system and 30 J of work is done on the system? Use [tex]\Delta U = Q - W[/tex].

A. -90 J
B. 90 J
C. 30 J
D. -30 J



Answer :

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].