# Thermodynamics Calculator

Let's start with couple of definitions: Heat is the amount of energy flowing from one body of matter to another spontaneously due to their temperature difference, or by any means other than through work or the transfer of matter. Historically, many energy units for measurement of heat have been used. The standards-based unit in the International System of Units (SI) is the joule (J). KCE-ThermoFluidProperties UG & Co. Hans-Joachim Kretzschmar Wallotstr. 3 01307 Dresden Germany. Tel.: +49-30 Mob.: +49-1.

This online calculator can solve thermodynamic equilibrium problems, such as finding the final temperature when mixing fluids, or finding the required temperature for one of the fluids to achieve a final mixed temperature. The only condition is that there should not be any phase transition (or phase change) of substances. To solve the problem, it uses the thermal equilibrium equation, more on this below.

Online calculator. This calculator can find missing values in the relationship between heat and temperature: heat added or removed, specific heat, mass, initial temperature and final temperature. You may be interested in other calculators in the Thermodynamics — Heat group: Air Pressure, Density, and Temperature vs. Altitude in Standard Atmosphere Calculator. Ideal Gas Law Calculator (Pressure–Volume–Temperature–Amount) Charles’s Law Calculator. Gay-Lussac Law Calculator. Avogadro’s Law Calculator.

## Thermal equilibrium equation

In the process of reaching thermodynamic equilibrium, heat is transferred from the warmer to the cooler object. Two objects are in thermal equilibrium if no heat flows between them when they are connected by a path permeable to heat, that is, they both have the same temperature. This is called the zeroth law of thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially and temporally uniform.

The thermodynamic system is called a thermally isolated system if it does not exchange mass or heat energy with its environment. In physics, the law of conservation of energy states that the total energy of an isolated system in a given frame of reference remains constant — it is said to be conserved over time.

The first law of thermodynamics can be stated as follows: during an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings. In the case of a thermally isolated system, we can say that during an interaction between objects inside a system (until it reaches thermal equilibrium), the amount of energy gained by one object must be exactly equal to the amount of energy lost by another.

This is our thermal equilibrium equation.

In another form:
,
where n – number of objects in the system.

That is, the algebraic sum of all heat quantities (gained and lost) in a thermally isolated system equals zero.

If we replace heat quantities with the formula described here: Quantity of heat, we will get the following equation:

### Thermodynamics Calculate Q

,
note that the final temperature for all substances (T1, T2, .. Tn) should be the same, because of thermal equilibrium.

This is the equation used by the calculator to find the unknown value. Also, the calculator can take into account the quantity of heat gained or lost to the surroundings. This allows a more broad range of problems to be solved.

To use the calculator, you need to correctly fill out the table describing interacting substances. The usage instructions for different scenarios are listed below the calculator. arrow_upwardarrow_downwardSubstancearrow_upwardarrow_downwardMass, kgarrow_upwardarrow_downwardSpecific heat, J/kg*Carrow_upwardarrow_downwardInitial temperature, Carrow_upwardarrow_downwardFinal temperature, C

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Last Updated: 5/28/2019

Usage, Disclaimer, Notes Brayton Cycle (Cold Air Standard) Template including Regeneration (Updated 3/22/2018)

This spreadsheet provides a template for analysis of the Brayton Cycle using the Cold Air Standard (constant specific heats).The user must fill in the data in the top grid.From that data, the cells in the second grid are updated, and Pressure-volume and Temperature-entropy diagrams are generated.Make sure your volume is set up high when you open it!A second sheet in the same workbook (not seen below but operating in a similar fashion) is set up to include Regeneration.For photos of aircraft powered by the Brayton cycle (Turbofans and Turboprops) as well as some powered by the Otto cycle, click here.

Rankine Cycle Template (Updated 6/18/2018)

This spreadsheet provides a template for analysis of the Rankine (steam) Cycle.The user must fill in the data in the top grid (from other software or table lookup).From that data, the cells in the second grid are updated, and Pressure-volume and Temperature-entropy diagrams are generated.For best results download the handy Excel “add-in” from Coolprop.That easy-to-implement add-in provides functions for all the properties of water you’ll need in completing this spreadsheet (and those of 150+ other fluids as well).The logic is not much different that manual table look-up and interpolation – provide two independent properties, e.g., P and Q (quality) and the function returns any of the others (U, T, H, S, etc.)Once you have implemented these functions properly, then the whole spreadsheet will update whenever any input parameter (those having the green background in the screen grab below) is changed.This spreadsheet includes a VBA function that (assuming you’ve automated the property evaluations using Coolprop or something similar) allows you to run a sequence of cases automatically to assess the sensitivity of one variable, e.g., the cycle efficiency, to another parameter, e.g., the turbine inlet pressure.

### Third Law Of Thermodynamics Calculator

Otto CycleTemplate (Updated 3/27/2018)

This spreadsheet provides a template for analysis of the Otto (spark-ignition, internal combustion) Cycle.The user must fill in the data in the top grid (from other software or table lookup).From that data, the cells in the second grid are updated, and Pressure-volume and Temperature-entropy diagrams are generated.If you use the thermal properties Excel add-in from CoolProp, then you can have the whole spreadsheet update whenever any input parameter is changed.This updated spreadsheet includes the capability of doing a sensitivity analysis.Turn up your volume before opening!For more on large aircraft engines using the Otto cycle, click here.

Diesel Cycle Template (Updated 3/15/2018)

This spreadsheet provides a template for analysis of the Diesel (compression-ignition, internal combustion) Cycle.The user must fill in the data in the top grid.From that data, the cells in the second grid are updated, and Pressure-volume and Temperature-entropy diagrams are generated.This workbook includes the capability of doing a sensitivity analysis.

Humphrey Cycle (New 5/3/2018)

You won’t find the Humphrey cycle in your thermo book.It involves a slight (in theory) modification to the Brayton cycle.The heat is added at constant volume instead of constant pressure.Thus the temperature rise in the combustion step is a factor of the ratio of specific heats higher than in the Brayton cycle.You will find that the increase in entropy is lower than that in the Brayton cycle and the cycle efficiency is correspondingly higher.If the practicalities can be worked out, the Humphrey cycle will be a “game changer.”

Vapor-Compression Refrigeration Cycle (New 5/2/2018)

The vapor-compression refrigeration cycle is analogous to the Rankine cycle, but runs in the opposite direction (counter-clockwise on the TS diagram vs. clockwise for the Rankine power cycle).This template uses R-134a as the working fluid, but can be readily changed to another refrigerant.

Mollier Diagram (New 6/5/2018)

The Mollier Diagram provides a useful way of depicting states and processes in a graphical format.This workbook for water allows you to plot points (obtained using the CoolProp Excel add-in directly) on a Mollier-Diagram found online at engineeringtoolbox.com.In theory you could use the CoolProp functions to create your own Mollier diagram from scratch, but Excel won’t allow you to plot that complicated a data set.

ProperT (New 10/23/2018, Version 2.0)

### Thermodynamics Calculator With Steps

The workbook uses the Coolprop Excel add-in to compute thermophysical properties of a baker’s dozen of fluids.The user can then plot the saturated liquid and saturated vapor lines in one of four common formats: (1) Temperature – entropy, (2) Pressure – volume, (3) Temperature – volume and (4) enthalpy – entropy (Mollier diagram).Using the model of Coolprop’s TextExcel.xlsm, this new edition includes a property calculator that uses units and nomenclature more frequently encountered in the study of engineering thermodynamics (kPa, kJ, specific volume, etc.).If you are analyzing a thermodynamic process or even a complete cycle, you can save the data returned by the property calculator and add it as another data series to the existing plot.

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