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Material Properties
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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.
ID:(786, 0)
Properties of Materials
Description
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 ($\Delta V$) 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)
Material Properties
Description
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.
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(ID 11151)
Examples
(ID 15271)
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 ($\Delta V$) 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)
(ID 15330)
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)
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} $ |
Here, $C_V$ represents the heat capacity at constant volume.
(ID 3603)
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)
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)
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 }$ |
(ID 3605)
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 $ |
(ID 3607)
ID:(786, 0)