A piston compresses the air in the cylinder by doing 61.0 J of work on the air. As a result, the air gives off 113.0 J of heat to the surroundings. If the system is the air in the cylinder, what is the change in its internal energy?

Explanation:

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In this case, since the first law of thermodynamics states that the heat added to system and the work done by the system are able to define the change in the internal energy as follows:

Since this problem shows that the system releases 113.0 J of heat, we use it negative as well as the 61.0 J of work performed on the system; therefore we write:

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