Fundamento
Enthalpy change
The molar integral is divided by the molar mass to give a mass basis.
\(\Delta h=\int_{T_1}^{T_2}c_p(T)\,dT\)
ThermoLab · Chapter 4
Energy integrals for closed systems
Integrates Cp(T), computes Δh and Δu, and evaluates polytropic boundary work.
Motor listo
Engineering results
NOT RUNDetailed calculation reportEquations · substitution · verification
Run the calculation to generate the report.
Engineering directory
13 linked modules on a single calculation base
Open any tool without losing your chosen unit system. Each page works on its own and keeps its navigation, report and export.
01
Appendices A-1 to A-28Universal property interpolator
→02Chapters 1 and 2Pressure, temperature and general energy balance
→03Chapter 3Pure substances and equations of state
→04Chapter 4Energy integrals for closed systems
→05Chapter 5Control volumes and the first law
→06Chapters 6 and 7Second law, Carnot and entropy
→07Chapter 8Exergy, destruction and second-law efficiency
→08Chapter 9Gas power cycles
→09Chapter 10Rankine steam power cycles
→10Chapter 11Refrigeration cycles
→11Chapters 12 and 13Gas mixtures and psychrometrics
→12Chapters 14 and 15Combustion and adiabatic flame temperature
→13Chapters 16 and 17Chemical equilibrium and compressible flow
→Engineering framework
Theory, equations and conditions of use
With a temperature-dependent Cp, the energy change is the area under the curve. Integration avoids assuming a constant specific heat outside a narrow range.
Fundamento
Simpson's rule
For an even number of subintervals, it weights the nodes 1-4-2-…-4-1.
\(I\approx\frac{\Delta T}{3n}[f_0+4f_1+2f_2+\cdots+f_n]\)
Fundamento
Boundary work
In a polytropic process P Vⁿ = constant, the work integrates in closed form.
\(W_b=\frac{P_2V_2-P_1V_1}{1-n}\)
Base documentalÇengel & Boles, 7th edition · SI appendices A-1 to A-28
USCS conversionA-1E to A-27E, via exact factors from the SI base
AlcancePreliminary design, teaching and independent verification
Engineering FAQ
Preguntas frecuentes
How many subintervals does Simpson's rule use?+
The engine uses 100, an even number that is sufficient for these smooth polynomials.
What happens if n=1?+
The isothermal form W=P₁V₁ ln(V₂/V₁) applies.
Are Δu and Δh the same?+
No. For an ideal gas, Δu=Δh-RΔT.