Draw isothermal, adiabatic, isobaric, and isochoric processes on PV diagrams. Calculate work, heat, and efficiency for cycles.
This is a drawing board for the four textbook ideal-gas processes - isothermal, adiabatic, isobaric, isochoric - rendered on a pressure-volume grid. You enter the gas amount and the endpoints of each leg; the tool plots the curves and reports the work, heat transfer, and thermal efficiency of any closed cycle you assemble. The thing students trip on: work is the area under the path on this diagram, so it depends on the route between two states, and its sign depends on direction. A clockwise loop delivers positive net work; run it backwards and every sign flips.
A concrete input and expected output from the current implementation.
Input
Carnot cycle, 1.0 mol ideal gas, R = 8.314 J/(mol K). Hot isothermal leg: 600 K, from 2.0 L to 4.0 L. Cold isothermal leg: 300 K.
Expected output
Efficiency: eta = 1 - TL/TH = 1 - 300/600 = 0.50 (50 percent). Heat absorbed at 600 K: QH = nRT ln(V2/V1) = 1.0 x 8.314 x 600 x ln 2 = 3457.7 J. Net work per cycle: W = eta x QH = 1728.8 J. Heat rejected at 300 K: QH - W = 1728.8 J. The hot isotherm is drawn from (2.0 L, 2.49 MPa) to (4.0 L, 1.25 MPa), with the cold isotherm and two adiabats completing the loop.
For a Carnot cycle, efficiency depends only on the reservoir temperatures, eta = 1 - TL/TH, which is exactly 50 percent because 300 K is half of 600 K. The isothermal work formula nRT ln(V2/V1) gives the heat absorbed, and net work is eta times that, so the rejected heat QH - W equals the net work when the efficiency is 50 percent.
Each leg is plotted from its governing relation: isobaric is a horizontal line at fixed P, isochoric a vertical line at fixed V, isothermal follows PV = constant, adiabatic follows PV^gamma = constant. Work for a leg is the integral of P dV, so the tool effectively measures the area beneath the curve; vertical legs contribute zero work.
For an ideal gas, internal energy depends only on temperature, so over a full cycle it returns to its starting value and net heat equals net work. The tool applies the first law leg by leg: isothermal legs exchange Q = W, adiabatic legs exchange Q = 0, isobaric legs split heat between work and internal energy change. Cycle efficiency is net work divided by heat absorbed.
Because the adiabatic legs change the gas temperature, and the gas must return to its starting state, so heat must be rejected at the cold temperature. The best possible efficiency is 1 - TL/TH, reaching 100 percent only as TL approaches absolute zero. The tool's Carnot result is an upper bound no real engine can beat.
Not exactly. The tool assumes an ideal gas with constant heat capacity, so the curves and numbers are wrong where real fluids deviate, especially near condensation. For steam and refrigerants, use property tables such as the NIST WebBook or a dedicated steam calculator, and treat the PV drawing as a schematic only.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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