Druyd:Knowledge

Material Properties

Storyboard

The material constants, whether for gases, liquids, or solids, typically represent the relationships between various variables. In this context, material constants correspond to slopes in different combinations of variables.

>Model

ID:(786, 0)

Mechanisms

Iframe

>Top

Knowledge

Code

Concept

Mechanisms

ID:(15271, 0)

Properties of Materials

Concept

>Top

Material properties generally describe how various variables change among them. The primary variables that characterize the state of a gas, liquid, and solid are:

• the pressure ( $p$ )
• the absolute temperature ( $T$ )
• the volume ( $V$ )
• the entropy ( $S$ )

The first two are intensive variables, meaning they do not depend on the size of the system. Therefore, any variation will simply be equal to:

• the pressure Variation ( $dp$ )
• the temperature variation ( $dT$ )

In the case of extensive variables, there is a dependence on the size of the system. Therefore, in this case, the variable must be normalized by dividing it by the system's size:

• the volume Variation ( $dV$ ) divided by the volume ( $V$ )
• the entropy variation ( $dS$ ) divided by the entropy ( $S$ )

Since the number of variables is fixed, there are only a limited number of alternatives and, consequently, constants.

ID:(589, 0)

Model

Top

>Top

Parameters

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$C_p$

C_p

Capacidad calórica con presión constante

J/K

$C_V$

C_V

Capacidad calórica con volumen constante

J/K

$k_p$

k_p

Compresividad isotermica

$\rho$

rho

Densidad

kg/m^3

$S$

Entropia

J/K

$p$

Presión

$T$

Temperatura

$k_T$

k_T

Thermic dilatation coefficient

1/K

$DV_{p,T}$

DV_pT

Variación de volumen en presión con temperatura constante

m^3/Pa

$DV_{T,p}$

DV_Tp

Variación de volumen en temperatura con presión constante

m^3/K

$c$

Velocidad del sonido

m/s

$V$

Volumen

m^3

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Calculations

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

Equation

$c ^2=\left(\displaystyle\frac{ \partial p }{ \partial \rho }\right)_ S$

c ^2= dp / drho

$C_p - C_V = n R$

C_p - C_V = n R

$C_p = T DS_{T,p}$

C_p = T * @DIFF( S , T , 1 , p )

$C_V = T DS_{T,V}$

C_V = T * @DIFF( S , T )

$k_p =-\displaystyle\frac{ DV_{p,T} }{ V }$

k_p =- DV_pT / V

$k_T =\displaystyle\frac{ DV_{T,p} }{ V }$

k_T = DV_Tp / V

ID:(15330, 0)

Constant pressure heat capacity

Equation

>Top, >Model

Specific heat capacity is defined as the change in temperature with respect to the supplied or extracted heat. It can be expressed by the equation:

$\delta Q = C_p dT = T dS$

This equation is an inexact differential because it depends on how the heat is supplied or extracted. In particular, when considering a constant pressure process, we define the heat capacity at constant pressure.

In other words:

$C_p = T DS_{T,p}$

where $C_p$ is the heat capacity at constant pressure.

ID:(3604, 0)

Constant volume heat capacity

Equation

>Top, >Model

The heat capacity is defined as the change in temperature with respect to the supplied or removed heat. It can be expressed using the equation:

$\delta Q = C dT = T dS$

This equation represents an inexact differential, as it depends on the manner in which the heat is supplied or removed. In particular, when considering a process carried out at constant volume, we define the heat capacity at constant pressure.

In other words:

$C_V = T DS_{T,V}$

$C_V$

Capacidad calórica con volumen constante

$J/K$

8779

$S$

Entropia

$J/K$

8776

$T$

Temperatura

$K$

8768

$V$

Volumen

$m^3$

8767

Here, $C_V$ represents the heat capacity at constant volume.

ID:(3603, 0)

Mayer's ratio for caloric capacity

Equation

>Top, >Model

The Mayer's relation states that the heat capacities of a gas at constant pressure and constant volume are related by the universal gas constant and the number of moles, as expressed by:

$C_p - C_V = n R$

Here, $C_P$ represents the heat capacity at constant pressure, $C_V$ represents the heat capacity at constant volume, $n$ is the number of moles, and $R$ is the universal gas constant.

ID:(11151, 0)

Isothermal compressibility coefficient

Equation

>Top, >Model

Compression is defined using as

$\kappa \equiv-\displaystyle\frac{1}{ V }\left(\displaystyle\frac{\partial V }{\partial p }\right)_ T$

When the notation is employed, the compressibility coefficient is defined as

$DV_{p,T} \equiv\left(\displaystyle\frac{ \partial V }{ \partial p }\right)_ T$

The compressibility coefficient itself is defined through as

$k_p =-\displaystyle\frac{ DV_{p,T} }{ V }$

ID:(3606, 0)

Coefficient of thermal expansion

Equation

>Top, >Model

Thermal expansion is defined using as

$k_T \equiv \displaystyle\frac{1}{ V } \left(\displaystyle\frac{\partial V }{\partial T }\right)_ p$

When the notation is employed, the coefficient of thermal expansion is defined as

$DV_{T,p} \equiv\left(\displaystyle\frac{ \partial V }{ \partial T }\right)_ p$

The coefficient of thermal expansion itself is defined through as

$k_T =\displaystyle\frac{ DV_{T,p} }{ V }$

$k_T$

Thermic dilatation coefficient

$1/K$

9361

$DV_{T,p}$

Variación de volumen en temperatura con presión constante

$m^3/K$

8772

$V$

Volumen

$m^3$

8767

ID:(3605, 0)

Sound velocity as a derivative of the pressure

Equation

>Top, >Model

Sound is an oscillation of density that propagates and is associated with a corresponding variation in pressure. Therefore, the speed of sound squared ( $m^2/s^2$ ) can be defined as the ratio of the pressure variation ( $Pa = kg/m s^2$ ) to the density ( $kg/m^3$ ). Due to the short time in which this occurs, it is assumed to be a variation at constant entropy. Thus, we can express it using as follows:

$c ^2=\left(\displaystyle\frac{ \partial p }{ \partial \rho }\right)_ S$

$\rho$

Densidad

$kg/m^3$

8775

$S$

Entropia

$J/K$

8776

$p$

Presión

$Pa$

8769

$c$

Velocidad del sonido

$m/s$

8774

ID:(3607, 0)