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Question 9.1: If 515 J of heat is added to a gas that does 218 J of work a......

If 515 J of heat is added to a gas that does 218 J of work as a result, what is the change in the energy of the system?

Strategy Energy flow occurs as either heat or work, and Equation 9.2 relates those to the total energy. We are given the magnitudes for q and w, but we must determine the direction for each process to assign the correct signs.

ΔE = q + w    (9.2)

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Heat added TO the system means that q > 0, so q = +515 J.

Work done BY the system means that w < 0, so w = –218 J.

ΔE = q + w = 515 J + (–218 J) = +297 J

Note that in most cases when a value is positive, the “+” sign is not placed in front of the number.

Discussion Though fairly simple numerically, this problem points to the need to consider the signs of q and w carefully.

Check Your Understanding 408 J of work is done on a system that releases 185 J of heat. What is the energy change in the system?

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