Exergy Calculator
Free Exergy Calculator for thermodynamics & heat. Enter variables to compute results with formulas and detailed steps.
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Where h and s are the specific enthalpy and entropy of the stream, h0 and s0 are values at the dead state (ambient conditions), T0 is the dead state temperature in Kelvin, V is velocity, g is gravitational acceleration, and z is elevation. For ideal gases, enthalpy and entropy differences are computed using specific heat and gas constant.
Last reviewed: December 2025
Worked Examples
Example 1: Steam Exergy in a Power Plant
Example 2: Compressed Air Exergy
Background & Theory
The Exergy Calculator applies the following established principles and formulas. Physics is the fundamental natural science concerned with matter, energy, and the interactions between them. Classical mechanics, founded on Newton's three laws of motion, provides the framework for analyzing the motion of objects. The first law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship: F = ma, where force equals mass times acceleration in SI units of newtons (N = kg·m/s²). The third law establishes that every action produces an equal and opposite reaction. Kinematics describes motion without reference to its causes. The four fundamental equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. These assume constant acceleration and are foundational for solving projectile motion, free fall, and linear dynamics problems. Energy conservation underpins much of physics. Kinetic energy is KE = ½mv², where m is mass in kilograms and v is speed in meters per second. Gravitational potential energy is PE = mgh, where g ≈ 9.81 m/s² near Earth's surface and h is height in meters. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE. Electricity and circuits rely on Ohm's law: V = IR, where voltage V is in volts, current I in amperes, and resistance R in ohms. Electrical power is P = IV = I²R = V²/R, measured in watts. Wave mechanics connects frequency f, wave speed v, and wavelength λ through f = v/λ, with frequency in hertz (Hz). Pressure is defined as force per unit area, P = F/A, in pascals (Pa = N/m²). The ideal gas law PV = nRT links pressure, volume, moles n, the gas constant R = 8.314 J/(mol·K), and absolute temperature in kelvin. Gravitational force between two masses follows Newton's law of universal gravitation: F = Gm₁m₂/r², where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant.
History
The history behind the Exergy Calculator traces back through the following developments. The history of physics spans over two millennia, beginning with the natural philosophy of ancient Greece. Aristotle (384–322 BCE) proposed that all matter consisted of four elements and that objects moved toward their natural place, with heavier objects falling faster than lighter ones. While largely incorrect, his systematic approach to explaining nature dominated Western thought for nearly 2,000 years. The Scientific Revolution overturned Aristotelian physics. Galileo Galilei (1564–1642) performed groundbreaking experiments on inclined planes and falling bodies, demonstrating that all objects fall with the same acceleration regardless of mass, and established the principle of inertia. His use of mathematics to describe motion was revolutionary. Isaac Newton synthesized these developments in his landmark Principia Mathematica (1687), laying out the three laws of motion and the law of universal gravitation. Newton's framework unified terrestrial and celestial mechanics, explaining planetary orbits with the same equations governing a falling apple. His calculus provided the mathematical language for expressing rates of change. The 19th century brought two major theoretical achievements. James Clerk Maxwell formulated his equations of electromagnetism between 1861 and 1862, unifying electricity, magnetism, and optics, and predicting the existence of electromagnetic waves traveling at the speed of light. Thermodynamics was developed by Carnot, Clausius, and Kelvin, establishing the laws governing heat, work, and entropy. The 20th century produced two revolutions that fundamentally altered the classical picture. Albert Einstein published the special theory of relativity in 1905, showing that space and time are not absolute but relative to the observer, and that mass and energy are equivalent via E = mc². His general theory of relativity in 1915 reinterpreted gravity as the curvature of spacetime. Simultaneously, quantum mechanics emerged from the work of Planck, Bohr, Heisenberg, and Schrödinger, revealing that at atomic scales energy is quantized and particles exhibit wave-particle duality. These developments culminated in the Standard Model of particle physics, which describes all known fundamental particles and three of the four fundamental forces.
Frequently Asked Questions
Formula
Exergy = (h - h0) - T0*(s - s0) + V^2/2 + g*z
Where h and s are the specific enthalpy and entropy of the stream, h0 and s0 are values at the dead state (ambient conditions), T0 is the dead state temperature in Kelvin, V is velocity, g is gravitational acceleration, and z is elevation. For ideal gases, enthalpy and entropy differences are computed using specific heat and gas constant.
Worked Examples
Example 1: Steam Exergy in a Power Plant
Problem: Steam enters a turbine at 500 C and 1000 kPa with a mass flow rate of 2 kg/s. The ambient conditions are 25 C and 101.325 kPa. Specific heat is 2.1 kJ/(kg*K). Calculate the specific physical exergy and total exergy rate.
Solution: T = 500 C = 773.15 K, T0 = 25 C = 298.15 K\nP = 1000 kPa, P0 = 101.325 kPa\nEnthalpy difference = cp * (T - T0) = 2.1 * 475 = 997.5 kJ/kg\nEntropy difference = cp * ln(T/T0) - R * ln(P/P0) = 2.1 * ln(773.15/298.15) - 0.287 * ln(1000/101.325)\n= 2.1 * 0.953 - 0.287 * 2.290 = 2.001 - 0.657 = 1.344 kJ/(kg*K)\nPhysical exergy = 997.5 - 298.15 * 1.344 = 997.5 - 400.7 = 596.8 kJ/kg\nTotal exergy rate = 2 * 596.8 = 1193.6 kW
Result: Specific Physical Exergy: 596.8 kJ/kg | Total Exergy Rate: 1193.6 kW
Example 2: Compressed Air Exergy
Problem: Air at 200 C and 800 kPa flows at 0.5 kg/s with velocity 30 m/s. Dead state: 25 C, 101.325 kPa. cp = 1.005 kJ/(kg*K). Find the total exergy flow rate.
Solution: Physical exergy = cp*(T-T0) - T0*[cp*ln(T/T0) - R*ln(P/P0)]\n= 1.005*175 - 298.15*[1.005*ln(473.15/298.15) - 0.287*ln(800/101.325)]\n= 175.875 - 298.15*[1.005*0.461 - 0.287*2.068]\n= 175.875 - 298.15*[0.463 - 0.594] = 175.875 - 298.15*(-0.131)\n= 175.875 + 39.06 = 214.9 kJ/kg\nKinetic exergy = 0.5*30^2/1000 = 0.45 kJ/kg\nTotal = (214.9 + 0.45) * 0.5 = 107.7 kW
Result: Physical Exergy: 214.9 kJ/kg | Kinetic: 0.45 kJ/kg | Total Rate: 107.7 kW
Frequently Asked Questions
What is exergy and how does it differ from energy?
Exergy, also known as available work or availability, is the maximum useful work that can be obtained from a system as it comes to equilibrium with its surroundings (the dead state). Unlike energy, which is always conserved according to the first law of thermodynamics, exergy can be destroyed through irreversible processes such as friction, heat transfer across finite temperature differences, and mixing. Energy tells you how much total energy a system contains, but exergy tells you how much of that energy is actually useful for doing work. A room-temperature lake contains enormous energy but nearly zero exergy because it is already at environmental conditions and cannot drive any work-producing process.
What is the dead state in exergy analysis?
The dead state is the reference condition at which a system is in complete thermodynamic equilibrium with its environment, meaning it has no potential to do any work. At the dead state, the system temperature equals the ambient temperature, the pressure equals atmospheric pressure, and the chemical composition is in equilibrium with the surroundings. The dead state conditions are typically chosen as 25 degrees Celsius (298.15 K) and 101.325 kPa (standard atmospheric pressure), though actual ambient conditions should be used for accurate analysis. A system at the dead state has zero exergy by definition. The choice of dead state significantly affects exergy calculations, so it must be clearly defined and consistently applied.
What are the components of total exergy?
Total exergy consists of four main components. Physical (or thermomechanical) exergy results from temperature and pressure differences relative to the dead state and is further divided into thermal and mechanical sub-components. Kinetic exergy is associated with the velocity of the system relative to the environment, calculated as one-half times mass times velocity squared. Potential exergy is due to elevation differences relative to a reference level, calculated as mass times gravity times height. Chemical exergy arises from differences in chemical composition between the system and the reference environment. For most thermodynamic analyses of power and refrigeration systems, physical exergy is the dominant component, while chemical exergy becomes important in combustion and chemical process analysis.
How is exergy analysis used in power plant optimization?
Exergy analysis identifies where the largest thermodynamic losses occur in power plants by quantifying exergy destruction in each component. In a typical coal-fired plant, the largest exergy destruction occurs in the combustion chamber (25-35 percent of fuel exergy), followed by heat exchangers (5-10 percent), the turbine (3-5 percent), and the condenser (2-4 percent). By identifying these major sources of irreversibility, engineers can prioritize improvements for maximum benefit. For example, preheating combustion air recovers exergy that would otherwise be lost in flue gases. Increasing steam temperature and pressure reduces exergy destruction in heat transfer. Exergy analysis has led to combined cycle plants achieving over 60 percent exergy efficiency.
What is exergy destruction and how does it relate to entropy generation?
Exergy destruction is the loss of potential work due to irreversibilities in a process, and it is directly proportional to entropy generation through the Gouy-Stodola theorem. The relationship is expressed as exergy destroyed equals T0 times entropy generated, where T0 is the dead state temperature in Kelvin. Every irreversible process generates entropy and simultaneously destroys exergy. Common sources of exergy destruction include heat transfer across finite temperature differences, fluid friction in pipes and turbomachinery, throttling and unrestrained expansion, mixing of streams at different temperatures or compositions, and chemical reactions proceeding irreversibly. Minimizing exergy destruction is the key objective in thermodynamic optimization.
What is the difference between exergy efficiency and energy efficiency?
Energy efficiency (first law efficiency) measures the ratio of useful energy output to total energy input, but it can be misleading because it treats all forms of energy as equivalent. Exergy efficiency (second law efficiency) measures the ratio of useful exergy output to total exergy input, providing a more meaningful assessment of thermodynamic performance. For example, an electric resistance heater has nearly 100 percent energy efficiency but only about 5 to 10 percent exergy efficiency because it converts high-quality electrical energy (pure exergy) into low-grade heat. A heat pump with a COP of 4 has 400 percent energy efficiency but about 20 to 40 percent exergy efficiency. Exergy efficiency always correctly identifies the thermodynamic quality of energy conversion.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy