Physical principles

Thermal analysis is a number of techniques in which the physical properties of a material are measured as a function of time, while the material is subjected to a controlled or programmed temperature change. Thermodynamics is the field of physics that underlies calorimetric investigations.


Thermodynamics is the study of the laws that govern the conversion of energy from one form to another, the direction in which heat will flow, and the availability of energy to do work. From the principles of thermodynamics one can derive general relations between such quantities as coefficients of expansion, compressibilities, specific heat capacities, heats of transformation, and magnetic and dielectric coefficients, especially as these are affected by temperature. The principles of thermodynamics also tell us which of these relations must be determined experimentally in order to completely specify all the properties of the system. The principal energy laws are derived from two famous laws of thermodynamics.

First law of thermodynamics

The first law of thermodynamics says that the total quantity of energy in the universe remains constant. This is the principle of the conservation of energy. Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the universe remains constant, merely changing from one form to another. The first principle establishes the equivalence of the different forms of energy (radiant, chemical, physical, electrical, thermal), the possibility of transformation from one form to another, and the laws that govern these transformations.

The state of a system can be changed by adding or subtracting heat or by performing work on the system. The function that depends on the state of the system is called internal energy (U), corresponding to the energy stored in the system at the molecular level. For a change of state of a system from A to B, the first law is expressed as:

DU = UB UA = q + w

where q is heat and w is work. In a process at constant volume:

(DU)V = q

In a process at constant pressure, a new quantity called enthalpy (H) is defined:

H = U +pV

where p is the pressure and V the volume.

Heat capacity is a very important quantity and is defined as the amount of heat q divided by the temperature increase
DT resulting from adding heat q to the system:

C = q / DT

For a process at constant volume:

Cv = (dU / dT)V

and for a process at constant pressure:

Cp = (dH / dT)p


Nicolas Leonard Sadi Carnot (1796-1832), French physicist and engineer, co-founder of thermodynamics

Benoit Paul Emile Clapeyron (1799-1864). French engineer, co-founder of thermodynamics

It was Rudolf Clausius (1822-1888) who declared that 'the entropy of the universe tends to a maximum'. Thus, natural systems tend to a state of equilibrium or maximum disorder or maximum entropy.

Second law of thermodynamics

The second law, known as Carnot's principle, is defined by the concept of entropy (S), introduced by Clapeyron. The second law states that the quality of this energy is degraded irreversibly. Entropy characterises the degree of disorder in a system. As energy is transferred from one form to another, some is lost as heat. Entropy is merely the way to measure the energy that disperses or spreads out in a process (as a function of temperature). Entropy always either increases or remains constant in a closed system.

The change in entropy (DS) is equal to the heat transfer (DQ) divided by the temperature (T):

DS = (DQ) / T

In the table below are some useful equations for thermal analysis and calorimetric techniques, especially for determination of heat capacity and specific heat capacity of materials.


Title Equation Terms

Heat capacity at constant pressure


Cp [J.K-1]

Cp = (dQ / dT)p

Cp = heat capacity at constant pressure

dQ = heat change (J)

T =  temperature (K)

p = pressure (Pa)

Heat capacity at constant volume


Cv [J.K-1]

Cv = (dQ / dT)v

Cv = heat capacity at constant volume (J.K-1)

dQ = heat change (J)

T =  temperature (K)

v = volume

Specific heat capacity at constant pressure


cp []

Cp = (1/m) (dQ / dT)p

cp = specific heat capacity at constant pressure (

dQ = heat change (J)

m = mass (kg)

T =  temperature (K)

p = pressure (Pa)

Specific heat capacity at constant volume


cv [J.m-3.K-1]

Cv = (1/V) (dQ / dT)v

cv = heat capacity at constant volume 

dQ = heat change (J)

V = volume (m3)

T =  temperature (K)

Ideal gas law

PV = n RT

P = gas pressure in Pa   

V = volume occupied by the gas in m3 

T = the temperature of the gas in Kelvin

R = the universal gas constant

(R = 8.3144 J mol-1 K-1)

Universal gas constant


R [J.mol-1.K-1]


R = 8.3144 J mol-1 K-1



S [J K-1]

S = dQ/T

S = entropy (J K-1)

dQ = heat change (J)

T = temperature (K)



H [J]

H = U + PV

H = enthalpy (J)

U = energy (J)

P = pressure (Pa)

V = volume (m3)