# Entropy Calculator

Created by Julia Żuławińska
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Dec 30, 2022

Although entropy is all about chaos and disorder, our entropy calculator is here to answer all your entropy related questions in a simple and organized way. In the following text, we will give an entropy definition, as well as a couple of ways of calculating entropy change. We'll explain the Gibbs free energy equation, the change in entropy formula for chemical reactions, and the isothermal process for gases that can be described by the ideal gas equation.

Have you ever heard someone saying that the universe tends toward chaos? Well, let's dive in that statement and find out what it means!

## Entropy - definition

The second law of thermodynamics states that:

🙋 The disorder of a system is always increasing.

Entropy is the measure of that disorder. But why measure disorder, and is it even possible? Physically, we can't measure entropy, but we can calculate it. It's one of the main determinants of the spontaneity of a reaction.

A spontaneous process is one that doesn't require an outside source of energy to proceed. It doesn't have to be a fast - it can even be still occurring when the heat death of the universe occurs - but if it would proceed without the addition of any outside energy, it's spontaneous.

It might sound complicated, but you'll understand it easily with an everyday example. Let's say you've made yourself a hot cup of coffee. You add some milk to it. You observed that the milk quickly mixes with the coffee. You intuitively know that the opposite process is not possible - the milk won't separate from coffee by itself.

Any spontaneous process increases the disorder of the universe. As stated by a physicist Rudolf Clausius: "The entropy of the universe tends to a maximum."

The entropy of a system is strictly connected to the systems energy. Every system tends toward stability, and, for an irreversible process, maximum stability is reached it when the system's energy is most disordered.

## How to calculate entropy change?

Entropy is a state function. This means that it is dependent on the entropies of the initial and final states of a system, not on the path the system takes. In chemistry, it's the difference between the entropy of the products and the reactants.

For chemical reactions, the change in entropy formula is:

$\small \Delta S_{\text{reaction}} = \Delta S_{\text{products}} - \Delta S_{\text{reactants}}$

Entropy (S) is normally measured in J/K, but standard entropy (So) is also used. This value is measured at 298.15 K and at a pressure of 1 bar. Its units are J/K*mol. The above equation can also be written in a standard entropy form:

$\small \Delta S_{\text{reaction}}^o = \Delta S_{\text{products}}^o - \Delta S_{\text{reactants}}^o$

Let's look at some standard entropy values:

Substance

Standard Entropy

H2 (gas)

131.0

O2 (gas)

205.0

H2O (gas)

188.7

H2O (liquid)

69.9

C (diamond)

2.4

As you see, gases have higher entropy than liquids and solids. It's because of the random movement of the molecules. On the other hand, diamond, a highly ordered solid, has entropy very close to zero.

## Gibbs free energy equation

What is Gibbs free energy? It's the energy in a system available to do work on its surroundings at constant pressure and temperature. It's a function of both enthalpy and entropy, and is used to predict the spontaneity of a processes. The Gibbs free energy equation is:

ΔG = ΔH - (T * ΔS),

where:

• ΔG is the change in Gibbs free energy.
• ΔH is the change in enthalpy.
• T is the temperature (in Kelvin).
• ΔS is the change in entropy.

Earlier, we talked about spontaneity of a process and how it is associated with entropy. We can also define it with regards to the change in free energy:

• ΔG<0 - a spontaneous process (a round boulder rolling down a hill).
• ΔG=0 - a system at equilibrium (a round boulder placed on a flat surface).
• ΔG>0 - a nonspontaneous process - additional energy must put in for the reaction to happen (a round boulder being pushed up a hill).

The direction of a free energy change can be either enthalpy- or entropy-driven. If:

• ΔH >> T * ΔS then the reaction is enthalpy-driven. The free energy comes mostly from a flow of thermal energy.
• ΔH << T * ΔS then the reaction is entropy-driven. The increase of disorder provides most of the free energy.

## Change in entropy formula - the isothermal process of an ideal gas

For the isothermal process of an ideal gas, entropy can be a function of both volume and pressure:

$\begin{split} \small \Delta S &= n \cdot R \cdot ln(\frac{V_2}{V_1}) \\ &= - n \cdot R \cdot ln(\frac{P_2}{P_1}) \end{split}$

, where

• $\small n$ is the number of moles.
• $\small R$ is the gas constant, 8.3145 J/mol*K.
• $\small V_2, V_1$ is the final and initial volume.
• $\small P_2, P_1$ is the final and initial pressure.

Isothermal processes are those that occur at a constant temperature. You might have met the base equation for a change in entropy in these conditions before: ΔS = ΔQ / T. In the equation above, we switched the change of heat (ΔQ) for values that will make calculations easier for you.

## Entropy properties

• When you heat up a gas in a closed container, you give the molecules additional energy. Now the molecules have more ways of spreading energy than before, so increasing temperature increases entropy (you can also use this method to measure and calculate lattice energy).

• If there is a chemical reaction that involves an increase in the number of gas molecules, entropy will rise.

• Substances with a simpler atomic structure will have lower entropy than more complex ones.

Have you enjoyed our entropy calculator? Would you like to know how entropy is used in statistics? Check out the Shannon entropy calculator next!

## FAQ

### How to calculate the entropy of a chemical reaction?

Use the change in entropy formula for reactions: ΔSreaction = ΔSproducts - ΔSreactants. You will need to find the change in entropy for the products and for the reactants. Then, you will need to subtract or add them in the Omnicalculator tool Entropy calculator.

### How much entropy there is in the cooling of 100 °C boiling water?

There is -1.01 kJ/K*kg. We will use the change in entropy formula: Δs = Cp × ln(Tf / Ti), where Tf and Ti indicate the final and the initial temperature, respectively.

1. Define final and initial temperature: Tf= 20 °C, Ti = 100 °C.
2. Solve the equation (specific heat at constant pressure Cp = 4.1818 kJ/K*kg).
3. The result is -1.01 kJ/K*kg.

### What is the entropy change when doubling the volume of an ideal gas?

It is 5.763J/K*kg. You can use the Omnicalculator tool Entropy or do as follows:

1. Use the change in entropy formula: ΔS = n * R * ln(V2/V1) considering n as the ideal gas moles equal to 1.
2. Notice that V2/V1 equals two because we are doubling the volume. Also, R is the ideal gas constant.
3. The result will be 5.763J/K*kg.

### What is an entropy definition in real life?

We can define entropy as a disorder. The more disorder we have in a system, the more entropy we find. For example, water at 20 °C has an entropy of 0.296 kJ/Kkg and at 100 °C, 1.307 kJ/Kkg. Note the higher entropy at a higher temperature (molecules have more energy).

Julia Żuławińska
Entropy change for a reaction
Total entropy of products
J
/mol*K
Total entropy of reactants
J
/mol*K
Entropy change for a reaction
J
/mol*K
Gibbs free energy ΔG = ΔH - T*ΔS
Change in enthalpy
J
Temperature
°F
Change in entropy
J
/K
Change in Gibbs free energy
J
Isothermal entropy change of an ideal gas
Base variable
volume
Amount of moles
mol
Initial volume
Final volume
Change in entropy
J
/K
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