A gas is contained in a cylinder with a movable piston. The gas is compressed by the piston, and during the process the gas releases 150 J of heat to the surroundings. The work done on the gas by the piston is 350 J. What is the change in the internal energy of the gas?
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Correct answer
A. 200 J
Principle or equation
The first law of thermodynamics states that the change in internal energy of a system equals the heat added to the system plus the work done on the system: ΔU = Q + W. Here Q is negative because heat is released, and W is positive because work is done on the gas.
Why this answer is correct
The gas releases heat, so Q = -150 J. Work is done on the gas, so W = +350 J. Thus ΔU = -150 J + 350 J = +200 J. The internal energy increases by 200 J.
Example
If a gas absorbs 100 J of heat and 50 J of work is done on it, ΔU = 100 J + 50 J = 150 J.
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