Calculate work, heat, internal energy change, and entropy for isothermal, isobaric, isochoric, and adiabatic processes. Includes energy balance visualization.
The four fundamental thermodynamic processes — isothermal, isobaric, isochoric, and adiabatic — describe how ideal gases transform between states. Each holds one variable constant, leading to dramatically different relationships between work, heat, and internal energy change. The first law of thermodynamics (Q = ΔU + W) connects them all.
In an isothermal process, temperature stays constant, so all absorbed heat converts to work (ΔU = 0). In an adiabatic process, no heat is exchanged, so work comes entirely from internal energy (Q = 0). Isobaric (constant pressure) and isochoric (constant volume) processes are the simplest to visualize on a PV diagram — horizontal and vertical lines, respectively.
These four processes are building blocks for real thermodynamic cycles: the Carnot cycle uses isothermal and adiabatic steps, the Otto cycle (gasoline engines) uses adiabatic and isochoric, and the Diesel cycle uses adiabatic and isobaric. Understanding each process individually is essential before analyzing cycles.
Use this calculator when you want to compare how heat, work, and internal energy behave under different thermodynamic constraints. It is especially useful for class exercises, engine-cycle analysis, and checking whether a worked solution satisfies the first law.
First Law: Q = ΔU + W. Isothermal: W = nRT ln(V₂/V₁). Isobaric: W = PΔV. Isochoric: W = 0. Adiabatic: PV^γ = const, W = (P₁V₁ − P₂V₂)/(γ−1).
Result: W = 69.3 kJ, Q = 69.3 kJ, ΔU = 0
Isothermal expansion from 0.5 to 1 m³ at 300 K: W = nRT ln(2) = (200×0.5) × ln(2) = 69.3 kJ. All heat absorbed equals work done, with no temperature change.
Isothermal processes keep temperature fixed and trade heat for work. Isobaric processes keep pressure fixed, so the volume change controls the work. Isochoric processes lock volume, which makes work zero. Adiabatic processes exchange no heat, so energy shifts entirely between work and internal energy.
When the numbers do not satisfy the first law, the usual cause is a sign convention issue. Check whether work is being treated as done by the system or on the system before concluding the setup is invalid.
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It is energy conservation for thermal systems: heat added equals the change in internal energy plus work done by the system.
Because no heat escapes during adiabatic compression, so the work done on the gas raises its internal energy and temperature.
Gamma is the heat capacity ratio Cp/Cv. It determines the steepness of the adiabatic relationship for an ideal gas.
Work is the area under the P-V curve. If volume does not change, the area is zero, so no work is done.
Idealized engine cycles are built from these same steps: Otto uses adiabatic and isochoric changes, Diesel adds an isobaric step, and Carnot uses isothermal and adiabatic steps.
Entropy measures how energy is dispersed. For a reversible process, dS = dQ/T; irreversible processes increase total entropy.