First law of thermodynamics

The first law of thermodynamics is conservation of energy for a system that can be heated, cooled or worked on: the change in internal energy equals the energy added by heating plus the work done on the system.

The AP Physics 2 sheet prints two equations that have to be read together:

ΔU=Q+WW=−PΔV\Delta U = Q + W \qquad W = -P \Delta V

In that pairing, WW is the work done ON the system. Every sign follows from that one decision. The minus sign in W=−PΔVW = -P\Delta V exists to enforce it: compress a gas and ΔV\Delta V is negative, so WW comes out positive, which correctly says energy went into the gas.

SituationSign
Gas is compressedW>0W > 0
Gas expandsW<0W < 0
Volume held fixedW=0W = 0
System is heatedQ>0Q > 0
System is cooledQ<0Q < 0

Many textbooks use the opposite convention, writing ΔU=Q−W\Delta U = Q - W with WW meaning the work done BY the gas. That version is internally consistent and gives identical answers, since the work on the gas is minus the work by the gas. What is wrong is mixing the two inside one problem: taking WW as positive for an expansion and then adding it produces an internal energy change with the wrong sign, and the arithmetic never flags it. Use the sheet's version on the exam and translate any other source first.

The CED states the law at 9.4.B.1 and then splits it. For an isolated system the total energy is constant (9.4.B.1.i). For a closed system, where energy may cross the boundary but matter may not, ΔU=Q+W\Delta U = Q + W (9.4.B.1.ii).

Reading work off a diagram, and handling cycles, belongs to the PV diagrams guide.

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