PV Diagrams & Work Conceptual Cycles Quiz

Concept: PV work equals area under the curve. Work is W = ∫PdV, which is the area under the curve. On a PV graph, a bigger area under the path means more work done by the gas.

Concept: Expansion means the gas does work outward. Expansion means the gas pushes outward and does work on surroundings. With positive pressure and increasing volume, the PV work is typically positive.

Concept: Compression means work is done on the gas. Compression means work is done on the gas, so work by the gas is negative. The surroundings push the piston inward, transferring energy to the gas.

Concept: A loop returns to the start state. A loop means the system returns to the initial state. The path closes because both P and V return to their starting values.

Concept: Enclosed area = net work for a cycle. The enclosed area is net work; direction sets the sign. Clockwise vs counterclockwise determines whether the gas does net work or has work done on it.

Concept: Clockwise loop = net expansion work. Clockwise direction corresponds to net expansion work. The gas tends to expand at higher pressure and compress at lower pressure, giving positive net area.

Concept: Counterclockwise loop = net work input. Counterclockwise typically indicates net work done on the gas. That’s common in refrigeration-type cycles where work must be supplied.

Concept: No volume change means no PV work. If ΔV=0, then W=∫PdV=0. On a PV diagram, this corresponds to a vertical line.

Concept: Vertical line means ΔV=0. No change in volume means no PV work. Even if pressure changes, the area under the curve is zero because there is no horizontal width.

Concept: Horizontal line = constant pressure. Horizontal means pressure stays the same. Work can still be done because volume changes along the horizontal line.

Concept: First law over a complete cycle. Over a cycle, ΔU=0, so net Q=net W. Any net heat added must appear as net work output (or vice versa).

Concept: Net Q equals net W for cycles. Over a cycle, net Q=net W. If the gas does +200 J of net work, it must have received +200 J of net heat overall.

Concept: Cycles can have net heat input and net work output. Net heat can be positive if the system produces net work. The only quantity that must be zero over a cycle is ΔU.

Concept: Heat engines produce net work. Engines produce net work, shown by positive loop area. This typically appears as a clockwise loop on the PV diagram.

Concept: Losses reduce useful PV work. Losses reduce effective pressure/volume work and shrink loop area. Making the cycle more reversible reduces losses, which would tend to increase, not reduce, the useful area.

Concept: Net work scales with enclosed area. Smaller area means less net work. A PV diagram is a direct visual way to compare work output between cycles.

Concept: Refrigeration requires work input. Refrigerators require work input, so net work by gas can be negative. On a PV plot, this often appears as a counterclockwise loop.

Concept: Counterclockwise loop = work input. Refrigeration requires net work input, typically counterclockwise. This indicates the surroundings do net work on the working substance.

Concept: PV diagram axes. PV diagram is pressure vs volume. The “area” refers to the region under the curve on the P-V plot.

Concept: Two key PV ideas. The core ideas are loop = cycle and area = work. PV diagrams are useful because they visually connect process paths to mechanical work.