Textbook Problem 4.B.7

[Ryan Khiev 1L]

I have a question about the following textbook question:

In a combustion chamber, the total internal energy change produced from the burning of a fuel is −2573 kJ. The cooling system that surrounds the chamber absorbs 947 kJ as heat. How much work can be done by the fuel in the chamber?

I said that the total energy available for work was 1,626 kJ, but the book says -1,626 kJ. I thought that the work done by the fuel would be positive, since it would have that energy available to use. Can someone explain why the answer is negative instead? Thank you!

[Ethan Hung 2A]

It's because work done or heat added to the surroundings is always a negative number.
The equation used to calculate internal energy is ∆U = q + w. If ∆U = −2573kJ and q = -947kJ, then w must be -1626kJ. This equation essentially states that the surroundings gain 947kJ (because the value is negative) and that 1626kJ of energy are available to do work on the [/u]surroundings[/u] (again because the value is negative).

[Brooke Gushiken 1B]

Hi! I think negative sign for the w value represents the fact that the system is doing work on the surroundings. Therefore, the system still has 1626 kJ to do work, but the negative denotes that it does/gives off work on the surroundings and not the other way around.