Understand the engineering model
What is First-Law Energy Balance?
Thermodynamic calculations track energy, heat, work, temperature, phase change, resistance, and ideal limits under a declared system boundary and sign convention.
Make every energy term and its sign visible so a balance cannot appear correct through hidden convention changes.
The relationship
Write the model before substituting values
Closed-system balance: Q−W=ΔU+ΔKE+ΔPE, with heat into and work by the system positive.
See the calculation
From measurement to engineering result
1System and state data2Energy or resistance model3Heat, work, or efficiency
Worked context
Read the output with its units
With 500 kJ heat in, 120 kJ work out, and no macroscopic energy change, internal energy rises 380 kJ.
Interpret with care
Important model boundary
The sign convention is explicit and applies to a closed-system accounting interval. Mass flow, enthalpy transport, chemical/nuclear energy, electrical detail, and property-state relations require other models.
A calculated value does not certify a component, material, installation, operating envelope, code requirement, or safety decision. Check measurements, signs, standards, uncertainty, and professional approval where consequences matter.
Browse Engineering & science for connected physical relationships.
Quick guide
How to use this calculator
- Choose the physical relationship and solve direction that match the known measurements rather than forcing unlike quantities into one formula.
- Enter every unit, sign, reference direction, geometry, material property, fluid property, temperature basis, coefficient, and idealization explicitly. The calculator normalizes compatible quantities internally and exposes intermediate values.
- Use reconciliation and companion outputs to catch entry mistakes, then retain the stated model boundary. A theoretical result is not a design approval, material certificate, equipment rating, or safety determination.
Calculation method
How the first-law energy balance calculator works
Make every energy term and its sign visible so a balance cannot appear correct through hidden convention changes.
Closed-system balance: Q−W=ΔU+ΔKE+ΔPE, with heat into and work by the system positive.
Worked example
First-Law Energy Balance example
With 500 kJ heat in, 120 kJ work out, and no macroscopic energy change, internal energy rises 380 kJ.
Closed-system balance: Q−W=ΔU+ΔKE+ΔPE, with heat into and work by the system positive.
Supported inputs
Precision and limits
Engineering-model boundary
The sign convention is explicit and applies to a closed-system accounting interval. Mass flow, enthalpy transport, chemical/nuclear energy, electrical detail, and property-state relations require other models.
Units and precision
Calculations normalize compatible inputs to SI, retain working precision, and round only for display. Very small and large nonzero values use scientific notation; displayed digits cannot create accuracy beyond the entered measurements and properties.
Decision boundary
This page solves the declared idealized relationship only. Verify applicable material data, operating conditions, geometry, loads, coefficients, standards, codes, manufacturer requirements, uncertainty, and professional approval before consequential use.
Category ownership
Generic mechanics, materials, fluid, aerodynamic, wave, and thermodynamic relationships live here. Trade-specific pipe, HVAC, motor, electrical, construction, automotive, radiation, statistical, chemical, and astronomical workflows remain with their established categories.
Privacy
Entered values and results stay in this browser and are not sent to analytics or third parties.
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