Answer and Explanation:
We can realize that the positive signs can be associated with the input of some form of energy into a system and the negative signs are associated with the output of some form of energy to a system.
- Work w is done by the system is negative because it refers to the output of work.
- Work w is done on the system is positive because it refers to the input of work.
- Heat q is lost to the surrounding is negative because it refers to a loss, an 'output' of heat.
- Heat q is gained from the surrounding is positive because it refers to the heat being absorbed by the system, an 'input' of heat.
- Internal energy ΔE increases is positive because we're getting energy to the system.
- Internal energy ΔE decreases is negative because we're losing that energy from the system.