# Poisson's constant

**Poisson´s constant** is the ratio of heat capacity at constant pressure *Cp* to heat capacity at constant volume .

It is denoted by a Greek letter (gamma) or (kappa)

## Equation:[edit | edit source]

- – Poisson's constant;
- – heat capacity at constant pressure;
- – heat capacity at constant volume;
- a – relevant specific heat capacities.

Because is always greater than , **Poisson´s constant is always greater than 1.**

## Adiabatic process[edit | edit source]

Poisson's constant makes it possible to describe adiabatic process:

- – gas pressure,
- – volume of gas,
- – Poisson´s constant.

## Ratio for an ideal gas[edit | edit source]

For an ideal gas, the heat capacity does not depend on temperature. Therefore, we can express the enthalpy as
and internal energy
. Thus, we can say that Poisson´s constant is the ratio of enthalpy to internal energy:

On the other hand, we can express heat capacities via Poisson's constant

,
where – universal gas constant.

## Poisson's number[edit | edit source]

In practice, the inverse value of Poisson's constant, the so-called **Poisson's number** is more often used. It is denoted by a Greek letter (in some sources ). The value is also dimensionless and for most materials takes on values from the interval 0 to 0.5. Applies to:

- – Poisson's number,
- – Poisson's constant,
- – relative deformation in the supporting direction (stress direction),
- – relative deformation in the transverse direction (perpendicular to the stress direction).

**Poisson's number** is independent of the direction of loading for isotropic materials. For anisotropic materials such as wood or composites, the Poisson's number is different along the direction of loading to the structure.

From the above definition, it follows that Poisson's number is always positive, because it represents the absolute value of the share of proportional deformations. Because it is true for most materials that they taper in the transverse direction when stretched, and thus

Some sources give a definition of Poisson's number in the form:

However, there are modern materials that expand when stretched in the transverse direction. Using the second relation, these materials have a negative Poisson's number.

### Values of Poisson's number for selected materials[edit | edit source]

Steel 0,27 to 0,30 concrete 0,20 rubber 0,50

### The relationship between modulus of elasticity[edit | edit source]

For an isotropic material, Poisson's number relates the modulus of elasticity in tension, the so-called Young's modulus, to the modulus of elasticity in shear according to the equation:

, where

- – modulus of elasticity in shear,
- – Young's modulus,
- – Poisson's number.

## Links[edit | edit source]

### Source[edit | edit source]

- http://www.pd.isu.ru/kosm/method/obsh/lab/2-8.pdf
- Feynman R.P., Leighton R.B., Sands M.: Feynmanovy přednášky z fyziky 1/3. Fragment Havlíčkův Brod. 2000