Thermodynamics Formulas: Enthalpy, Entropy & Mayer’s Formula

Thermodynamics formulas include Entropy, Heat capacity, Isothermal Processes, Adiabatic processes, among many others.

• The study of the transfer of heat and other aspects of energy from one substance to another is called Thermodynamics. 
• How matter changes when heat and energy are applied to a particular substance or object is the study of Thermodynamics. 
• Any substance comprises atoms and molecules. 
• A thermodynamic system is a system with defined boundaries and surroundings and the transfer of temperature(T), Pressure(P), and Volume(V) between atoms and molecules.

Key Terms: Thermodynamics, Isothermal Process, Adiabatic Process, Heat Capacity, Quasi-Static Process, Energy, Heat, Temperature, Work

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What is Thermodynamics?

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Thermodynamics is one of the many branches of Physics that deals with the transfer of work, temperature, heat, and energy from one substance to another or from one form to another. 

• Some thermodynamic systems that can be found in our everyday life are, Air conditioners, Refrigerators, washing machines, and all other heating and cooling systems, which function on the principles of Thermodynamics.
• The laws of thermodynamics defines how a system’s energy changes, alongside whether the system can perform efficient work on its surroundings. 
• It simply explains how thermal energy is converted to or from different forms of energy, and how matter has been affected due to it.

There are numerous Thermodynamic formulas, including Enthalpy of Vaporization formula, Entropy formula, Adiabatic process, among many others.

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Enthalpy of Vaporization Formula

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Enthalpy of Vaporization is the quantity of energy required to turn a liquid substance into its gaseous form. It is also known as Heat of Vaporization or Heat of Evaporation. It is denoted by ΔHvap. The formula for Heat of Vaporization is,

ΔH_vap = ΔU_vap + pΔV

Where,

• ΔU_vap= increased internal energy and
• pΔV= work done under ambient pressure

The SI unit for the heat of vaporization is J or Cal

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Entropy Formula

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Entropy can be defined as the measure of the randomness and disturbance in the system. 

• Entropy is highest if the boundaries of the system are not defined. 
• Solid substances or closed-space substances will have less entropy whereas gaseous substances will have high entropy. 
• The entropy of a substance depends on two factors- Heat and Temperature.
• Entropy changes according to the temperature applied. 
• A lower temperature is equal to More entropy whereas a Higher Temperature applied is equal to Less Entropy. 
• Hence we can say that Entropy is inversely proportional to the temperature applied to the system. So to put it in a formula,

where, q_(rev) is the heat applied on the system.

The SI unit for entropy is J/K

Boltzmann’s Entropy Formula

Boltzmann’s Entropy formula talks about the relationship between the entropy of the system and the atoms and molecules arranged in the system. It is formulated as:-

S = k_b log W

‘kb ‘is Boltzmann’s constant which is equal to 1.380649 x 10^-23 J/K and ‘log’ is the natural logarithm function and W is the microscopic configurations. ‘W’ can also be written as Ω (Omega).

Read More: Boltzmann Equation: Statement, Equation, Applications and Examples 

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Law of Thermodynamics

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There are two Laws of Thermodynamics. All the thermodynamics systems and processes obey both the law of thermodynamics.

First Law of Thermodynamics

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’. It states the relationship between work, heat, and internal energy between molecules of the system. 

First law of thermodynamics

The work of a thermodynamics system can be calculated as negative external pressure applied on the thermodynamic system into the change of volume of a thermodynamic system, W= -p ΔV

The first law of thermodynamics can be represented as:

•  ΔU is the net sum of the internal change of energy of the system.
• Q is the sum of the heat between the system.
• And work is the quantity of energy exchanged between thermodynamics.

The first law of Thermodynamics is also called as ‘Law of Conservation of Energy

Second Law of Thermodynamics

The Second Law of Thermodynamics states that the ‘Entropy of an isolated system will never be zero’. It can also be represented mathematically as

Here, S represents the entropy.

The second Law of Thermodynamics is also called as Law of Increased Entropy.

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Heat Capacity Formula

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The heat capacity formula can be denoted as the product of mass, specific heat and the change in the temperature. It can be shown as, Q = mc Δ T.

Here, 

• m is the mass of the substance
• T is the change in the temperature of the substance and
• C is the Specific Heat Capacity of the substance.

Specific Heat Capacity Formula

Specific heat is defined as the heat required to change the temperature of a substance by 1 °C. The substance should not be of changing volume.

Hence the specific heat capacity formula can be associated with the energy required to change the temperature of a substance by 1 unit respective of 1kg mass volume of the substance. The formula of Specific heat Capacity is: 

Hence,

C = \(\frac{Q}{mΔt}\)

• Here Q is the heat energy applied
• m is the mass of a substance in kg
• and t is the temperature change

The changes in temperature can be calculated as

Δ T = (T_f – T_i)

Where T_f is the final temperature and T_i is the initial temperature in K.

The SI unit for the Specific Heat Capacity formula is J/Kg.K or J/Kg.^oC

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Thermodynamic Processes

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The many Thermodynamic Process include:

Isothermal Process

Isothermal Processes are those processes where the temperature of the system remains constant. The equal amount of transfer of heat between the inside and outside of the system maintains the state equilibrium and temperature constant. The pressure and volume of the system can change or vary the in Isothermal process.

Quasi-Static Process

Changes in the system happen very slowly in Quasi-Static Process. The changes in temperature, pressure, or volume are slower. Physically these processes do not show any changes for a long time and chemically they maintain a state of thermodynamic equilibrium.

Reversible Process

As the name suggests, Reversible Processes are processes in which change in the substance and its surroundings can be restored to its initial state by retracing the steps and following a reverse path.

Adiabatic Process

Adiabatic Processes are processes where there is no transfer of Heat. No exchange of heat takes place during the compression or decompression of the system. Such a process can be either reversible or irreversible. The

Adiabatic Process formula is:

Here, 

• P is the pressure applied to the system
• V is the volume of the system and
• \(\gamma\) is the Adiabatic Index.

Adiabatic Index can be calculated as the ratio of heat capacity at constant value C_p to the heat capacity at constant volume C_v.

Work in an Adiabatic Process: 

Work done in an Adiabatic Process depends on the pressure and volume of the substance. Similar to the Adiabatic process formula which depends on Pressure and Volume. The work done in an Adiabatic process can be calculated as

W = ∫ Pdv

• Where W is equal to the work done
• P is the pressure applied on the substance whereas
• V is the volume of the substance

Read Also: Adiabatic Process Derivation: Formula, Examples & Equation 

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Mayer’s Formula

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Mayer’s Formula explains the relationship between molar specific heat of a gas at constant pressure and volume.

Consider one mole of gas. Let us assign ‘P’ as Pressure, ‘V’ as Volume, and ‘T’ as Temperature.

Let there be the change in temperature from T to dT at constant volume applied on the gas.

Considering First Law of Thermodynamics-

ΔU=ΔQ -ΔW

ΔQ= ΔU+ ΔQ

= ΔU + PΔV

Since we are considering Volume as constant, ΔV=0

Hence ΔQ= ΔU

C_v = (ΔQ/ΔT)_v

C_v = (ΔU/ ΔT) _v

C_v = (ΔU/ ΔT) _v

Now, considering Pressure as constant,

ΔQ= ΔU+PΔV

C_p= (ΔQ/ ΔT) _p

C_p= (ΔQ/ ΔT)_p + P(ΔV/ΔT)_p

C_p= (ΔQ/ ΔT)_p + P(ΔV/ΔT)_p

Now for an ideal molar gas,pressure,volume will be equal to gas constant and temperature

PV=RT

ΔV/ΔT=R/P

C_p=(ΔU/ ΔT)_p + P*R/P

C_p= C_v + R

This is known as Mayer’s formula and the SI unit for Cp,Cv and R is joule/mole oC

Read Also:

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Things to Remember

• All the processes which occur in nature are guided by Thermodynamics laws.
• Adiabatic Processes are processes where there is no transfer of Heat.
• Boltzmann’s Entropy formula talks about the relationship between the entropy of the system and the atoms and molecules arranged in the system.
• Mayer’s Formula can be represented as, C_p = - C_v = R.
• Specific heat Capacity can be represented as, Specific Heat Capacity, = Energy Required / Mass ΔT.
• Enthalpy of Vaporization can be shown as, ΔH_vap=ΔU_vap+ pΔV.

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Previous Year Questions

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