When a system is heated, heat is by the system. the amount of heat added is given a sign. when a system is cooled, heat is by the system. the amount of heat is given a sign. if a gas expands, it must push the surrounding atmosphere away. thus, work is done the system and is given a sign. if a gas is compressed, then work is done the system. this work is given a sign.

First of all, we need to write the First Law of thermodynamics assigning the correct sign convention:

where

is the change in internal energy of the system

Q is the heat absorbed/released

W is the work done

and the signs are assigned based on whether there is an increase in the internal energy or not. Therefore:

Q is positive if it is absorbed by the system (because internal energy increases)

Q is negative if it is released by the system (because internal energy decreases)

W is negative if it is done by the system on the surrounding (because internal energy decreases)

W is positive if it is done by the surrounding on the system (because internal energy increases)

Using these definitions, we can now fill the text of the question:

When a system is heated, heat is ABSORBED by the system. The amount of heat added is given a POSITIVE sign. When a system is cooled, heat is RELEASED by the system. The amount of heat is given a NEGATIVE sign. If a gas expands, it must push the surrounding atmosphere away. Thus, work is done BY the system and is given a NEGATIVE sign. If a gas is compressed, then work is done ON the system. This work is given a POSITIVE sign.

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