First Law of Thermodynamics (Open System, Steady Flow) Calculator

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Overview

The First Law of Thermodynamics for open systems, also known as the steady-flow energy equation, is a fundamental principle stating that energy is conserved. For a steady-flow system, the rate of energy entering the system must equal the rate of energy leaving the system plus the rate of energy accumulation within the system (which is zero for steady state). This equation accounts for heat transfer, work transfer, and the energy carried by mass flow, including enthalpy, kinetic, and potential energy components. For the purpose of this calculator, a single inlet and single outlet are assumed.

Symbols

Variables

$\dot{Q}$ = Heat Transfer Rate, $\dot{W}$ = Work Transfer Rate, $\dot{m}$ = Mass Flow Rate, $h_{in}$ = Specific Enthalpy (Inlet), $h_{out}$ = Specific Enthalpy (Outlet)

Apply it well

When To Use

When to use: Apply this equation to analyze devices like turbines, compressors, nozzles, diffusers, heat exchangers, and pumps where mass flows in and out of a control volume. It is crucial for calculating energy transfer rates, determining unknown fluid properties at inlets or outlets, or sizing components in power plants and refrigeration cycles. Ensure the system is at steady state and identify all energy interactions.

Why it matters: This law is the bedrock of thermal system design and analysis in engineering. It enables engineers to predict performance, optimize efficiency, and troubleshoot energy-related issues in a vast array of applications, from power generation to HVAC systems and chemical processes. Its mastery is essential for developing sustainable and efficient energy solutions.

Avoid these traps

Common Mistakes

• Incorrectly applying sign conventions for heat and work.
• Forgetting to include all energy forms (enthalpy, kinetic, potential) or assuming they are negligible when they are not.
• Mixing units (e.g., using kJ for enthalpy and J for kinetic energy without conversion).
• Applying the equation to unsteady-flow systems without modification.

One free problem

Practice Problem

A steam turbine operates under steady-flow conditions. Steam enters at an enthalpy of 2800 kJ/kg and velocity of 50 m/s at an elevation of 10 m. It exits at an enthalpy of 2600 kJ/kg and velocity of 150 m/s at an elevation of 5 m. The mass flow rate is 2 kg/s, and the turbine produces 50 kW of work. Calculate the rate of heat transfer to or from the turbine.

Solve for: $Q_{d}ot$

Hint: Remember to convert kinetic and potential energy terms to kJ/kg by dividing by 1000.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Fundamentals of Heat and Mass Transfer by Incropera, DeWitt, Bergman, Lavine, 7th Edition
2. Thermodynamics: An Engineering Approach by Yunus A. Cengel and Michael A. Boles, 8th Edition
3. Transport Phenomena by R. Byron Bird, Warren E. Stewart, and Edwin N. Lightfoot, 2nd Edition
4. Wikipedia: First law of thermodynamics
5. Moran & Shapiro, Fundamentals of Engineering Thermodynamics
6. Cengel & Boles, Thermodynamics: An Engineering Approach
7. NIST CODATA
8. Cengel and Boles Thermodynamics: An Engineering Approach