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Thermodynamics Formulas

Introduction to Thermodynamics

Last updated date: 17th Mar 2023
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The principles of thermodynamics have wide generality, making them relevant to all physical and biological systems. The laws of thermodynamics arose quickly during the 19th century in response to the necessity to maximize the performance of steam engines. The rules of thermodynamics, in particular, provide a comprehensive explanation of all changes in a system's energy state and its ability to do beneficial work on its surroundings.

What is Thermodynamics?

Thermodynamics can be defined as the branch of physics that deals with the study of the relation between heat and other forms of energy, the subject also encompasses the relation between heat, work, temperature, and energy. The major thermodynamics equation is listed below.

Specific Heat Capacity Formula

Specific heat can be defined as the quantity of heat required to raise the temperature of 1 gram of a compound by one degree celsius. The unit of specific heat is Joule/Kg Kelvin (J/Kg K). The mathematical equation for specific heat capacity formula is

$C = \frac{\bigtriangleup Q}{m\bigtriangleup T}$

In this equation, C represents, specific heat

ΔQ represents the heat gained or lost during the reaction. (Heat capacity)

ΔT represents the temperature difference

m represents the mass

ΔT represents the change in temperature. It is calculated by

ΔT = (Tf - Ti), where Tf is the final temperature and Ti is the initial temperature.

Heat Capacity Formula

The heat capacity and the specific heat can be calculated by rearranging the equation for specific heat. The mathematical equation is as follows

Q = mcΔT

Q represents the heat capacity.

M represents the mass.

ΔT represents the change in temperature.

And c is the specific heat of the compound.

Adiabatic Process Formula

The adiabatic process can be defined as the process during which there is no exchange of heat between the system and surroundings. The energy is neither transferred nor exchanged in compression or expansion of the system. The adiabatic process is found to be both reversible and irreversible in nature. The mathematical equation for the adiabatic process formula is

PV𝛾= constant

In this equation, P represents the pressure of the system.

V represents the volume of the system.

γ represents the adiabatic index.

The adiabatic index is defined as the ratio of heat capacity at constant pressure Cp to heat capacity at constant volume Cv.

Work Done in Adiabatic Process Formula

As the concept of the adiabatic process is understood, the work done in an adiabatic process is dependent on the variables of the adiabatic process formula. The variables of the equation are pressure and volume, the equation for work done in an adiabatic process is given by,

W = ∫ Pdv

W represents the work done during the process

P represents the pressure of the system

V represents the differential volume of the system.

Enthalpy of Vaporization Formula

Enthalpy of vaporization is also termed as the heat of vaporization. It is used to define the amount of heat required to be absorbed to vaporize a specific quantity of a substance (which is liquid) at a constant temperature. The mathematical representation of the enthalpy of vaporization formula is as follows,


In this equation, Hv represents the heat of vaporization

q represents the heat

And, m represents the mass of the substance.

The First Law of Thermodynamics Formulas

The first law of thermodynamics states that “the energy can neither be created nor be destroyed, it can only be changed from one form to another.” Since thermodynamics encompasses the relationship between heat and work and heat is considered as a form of energy, all the thermodynamic processes must follow the laws of thermodynamics. The mathematical equation used to represent the thermodynamics formula of the first law is,

ΔU = q + w

Where ΔU represents the net change in the internal energy of the system.

q is the algebraic sum of heat exchanged between the system and surroundings.

w represents the work done by the system or on the system.

Work is also expressed as equal to the negative external pressure on the system multiplied by the change in volume, the mathematical expression is

w = -pΔV

Where p is the pressure applied on the system

ΔV is the change in the volume of a system due to pressure applied.

This mathematical equation is specifically known as the pressure-volume work.

The Second Law of Thermodynamics Formula

The second law of thermodynamics is also known as the law of increased entropy. The law states that the entropy of an isolated system will never decrease to zero. In other words, the entropy of any given isolated system will always increase. The mathematical equation used to represent the second law of thermodynamics formula is,

ΔSuniv = ΔSsys + ΔSsurr ≥ 0

Where S represents the entropy.

Entropy Formula

Entropy is the measure of randomness in a system. The standard unit for entropy is joules per kelvin (J/K). the mathematical representation of entropy formula is,

S = Kb ln(Ω)

Where S represents entropy.

Kb represents Boltzman’s constant

ln represents the natural log.

Ω (Omega) represents the number of microscopic configurations.


Thermodynamics is the branch of science that deals with the study of heat and work. There are three main laws of thermodynamics named the first, second and third laws. These laws govern all the physical processes of the system. The important formulas of thermodynamics include specific heat, entropy and adiabatic processes that are explained in the article.

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FAQs on Thermodynamics Formulas

1. What is the Kelvin Planck Statement?

The second law of thermodynamics is explained by the Kelvin-Planck statement, according to this statement, “it is impossible for any device that operates in a cycle to receive heat from a single reservoir and produce a net amount of work.” In other words, it is not possible to create a cyclically operating heat engine.

2. What is Entropy?

Entropy is defined as the degree of randomness of the universe. In other words, it can also be defined as the system's thermal energy per unit temperature that is not available for doing useful work. Entropy increases as disorderness increases in the system.

3. What is a specific heat capacity?

The specific heat capacity is the amount of heat that is required to increase the temperature of 1 Kg of the compound by one degree Celsius or 1 Kelvin. We know that when a substance absorbs heat energy, its temperature rises. When the same amount of heat is applied to equal masses of different substances, the temperature rise is observed to be different for each substance. Because different substances have different heat capacity.