Thermodynamics Calculator
Evaluate ideal gas states, isentropic processes, and power-cycle performance — Rankine thermal efficiency, turbine and compressor work, and Carnot limits — with benchmark-verified results.
PV = mRT · η_th = (w_t − w_p)/q_in
ThermoCore evaluates fluid states and full power cycles — ideal gas, isentropic compression, and Rankine efficiency — benchmark-verified against 88 reference problems.
The Two-Property Rule
Every thermodynamics calculation starts the same way: fix the state. For a pure substance, two independent intensive properties — such as P and T, or T and quality x — define everything else. Ideal gases then close the algebra with PV = mRT; steam needs property tables or an equation of state.
State → any two of P, T, v, u, h, s, x
Device → steady-flow balance w_t = h₁ − h₂ (turbine), w_c = h₂ − h₁ (compressor)
Cycle → η_th = w_net/q_in, screened against the Carnot ceiling 1 − T_C/T_H
Benchmark-Verified Examples
Superheated water state
Çengel & Boles A-6
Water at P = 5 MPa, T = 400 °C
Rankine cycle efficiency
88/88 benchmark set
Boiler 8 MPa / 500 °C · condenser 10 kPa · η_t = 0.88 · η_p = 0.85
Air compressor (isentropic)
88/88 benchmark set
Air 100 → 800 kPa · T₁ = 25 °C · η_c = 0.85 · k = 1.4
T1-001 is read directly from the Çengel & Boles steam tables (A-6): at 5 MPa and 400 °C the water is superheated with h = 3195.7 kJ/kg and s = 6.6483 kJ/(kg·K). T3-001 is a full Rankine cycle solved against an 88-problem benchmark — the 34.6% thermal efficiency and 1107.5 kJ/kg net work are reproduced exactly by the engine, never asserted. T2-006 applies the isentropic relation with η_c = 0.85 to find the real compressor outlet.
Engineering Formulas & Governing Equations
Ideal Gas Law
Equation 01Air has R = 287 J/(kg·K). Valid when the fluid behaves as a perfect gas — low pressure, high temperature, no phase change.
Cold-Air Standard Assumptions
Equation 02Constant specific heats evaluated at room temperature — the standard shortcut for air-standard cycles.
Entropy Change of an Ideal Gas
Equation 03The general relation for a pure ideal gas between any two states — zero for an isentropic process.
Isentropic Relations
Equation 04Holds for ideal gases with constant specific heats undergoing reversible adiabatic (isentropic) processes.
Turbine Work (Steady Flow)
Equation 05Specific work from a single-inlet/single-outlet adiabatic turbine equals the enthalpy drop across it.
Rankine Cycle Thermal Efficiency
Equation 06Net work per unit heat added; the back-work ratio bwr = w_pump/w_turbine is small but never zero for real plants.
Carnot Limits
Equation 07The maximum efficiency of any heat engine between reservoirs, and the maximum refrigerator COP.
Calculation Details & Clarifications
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