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.
This calculator is essential for thermodynamics coursework, HVAC engineering, and engine design. Instead of manually solving for each state variable, enter initial conditions and the constraint — the calculator handles all derived quantities and verifies the first law balance. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
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.
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Conservation of energy for thermal systems: Q (heat added) = ΔU (internal energy change) + W (work done by the system). Energy in = energy stored + energy out.
In adiabatic compression, no heat escapes. All work done on the gas goes to increasing its internal energy (temperature). In isothermal, the gas continuously dumps heat to stay cool.
The heat capacity ratio Cp/Cv. It determines how much temperature changes during adiabatic processes. Higher γ means a steeper adiabatic curve on the PV diagram.
Work = ∫P dV. If volume doesn't change (dV = 0), no work is done regardless of pressure changes. All heat goes to internal energy.
Otto cycle (gasoline): 2 adiabatic + 2 isochoric steps. Diesel: 2 adiabatic + 1 isobaric + 1 isochoric. Carnot: 2 isothermal + 2 adiabatic.
A measure of thermal disorder. dS = dQ/T for reversible processes. Entropy increases in irreversible processes — the second law of thermodynamics.