PV Diagram Quiz: Test Your Knowledge Of Thermodynamic Cycles

Concept: work on pv graphs. For a gas process, (w) corresponds to the integral of (p,dv), which is the area under the curve. This is why pv plots are so useful for engines.

Concept: cycle work as enclosed area. A full cycle returns to the starting state, so the net work equals the enclosed loop area. The direction of the loop indicates whether the system produces work or consumes work.

Concept: loop direction. Clockwise cycles generally indicate the gas does positive net work on the surroundings. Counterclockwise loops usually indicate work input (refrigerator/heat pump).

Concept: cycles return to the start. In a cycle, the system returns to its initial state. That’s why state variables (like (p, v, t)) end where they began.

Concept: expansion vs compression. Expansion means the gas takes up more volume. Engines often produce work during expansion.

Concept: work sign. Compressing a gas typically means pushing on it, transferring work into the gas. In cycles, some steps require work while others deliver work.

Concept: work equals area. Larger enclosed pv area corresponds to more net work per cycle. This is a qualitative design goal for many engine cycles.

Concept: isochoric process. Volume is fixed on a vertical line. Pressure can change while volume stays constant.

Concept: isobaric process. Pressure is fixed along a horizontal line. Volume changes while pressure remains the same.

Concept: heat addition at high t. Adding heat at higher temperatures can improve theoretical efficiency. Many ideal cycles arrange heat input to happen at higher temperature stages.

Concept: state function over a cycle. Internal energy depends only on state, not path. Since the state returns to the start, (\delta u = 0) over the full cycle.

Concept: first law for cycles. Over a cycle, (\delta u = 0), so (q_{net} = w_{net}). Net heat added equals net work delivered.

Concept: isothermal meaning. Isothermal means temperature stays constant during the process. It’s an idealisation used in some cycle models.

Concept: pv shows work, not heat directly. Work is linked to (p,dv) and thus pv area. Heat depends on the path and internal energy changes, so it needs thermodynamic information beyond just geometry.

Concept: work sign via loop direction. Counterclockwise loops mean the surroundings do net work on the gas. That matches refrigeration cycles requiring electrical input.

Concept: units check for work. Pressure times volume has the same units as energy. This supports the interpretation of pv loop area as work.

Concept: efficiency definition. Efficiency is (w/q_{in}). Increasing (w) while keeping (q_{in}) fixed increases efficiency.

Concept: real vs ideal cycles. Ideal cycles assume perfectly controlled steps and no losses. Real engines have irreversibility that changes the pv loop and reduces work output.

Concept: work per cycle. The pv loop area corresponds to net work. Efficiency depends on both work and heat input, but area is directly tied to work.

Concept: visual comparison tool. pv diagrams let you see expansions, compressions, and net work at a glance. They’re a standard way to compare cycle shapes and expected work output.