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The temperature of the soil depends on its heat capacity and the heat transfer to or from the soil surface. The heat capacity is influenced by the soil's composition and the amount of water and water vapor it contains.

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Concept

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Description

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Heat is nothing more than energy at a microscopic level.

In the case of a gas, it corresponds primarily to the kinetic energy of its molecules.

In liquids and solids, we must take into account the attraction between atoms, which is where potential energy comes into play. Therefore, in these cases, heat corresponds to the energy that particles have and with which they oscillate around the equilibrium point defined by the surrounding particles.

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Description

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Temperature is the parameter we use to measure the heat energy contained in an object. Since heat energy can never be negative, it is essential to work with the Kelvin scale, where its zero point corresponds to the complete absence of this energy.

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Description

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Heat is associated with elements like fire, which causes the temperature of water to rise. The process of heating generates movement, indicating that heat is related to mechanical energy. Even the handle of a pot gets heated, and our bodies are capable of perceiving that temperature. Moreover, fire emits radiation that heats up objects that are exposed to it.

From this, we can infer that by transferring heat, we can raise the temperature of an object, and that the generation of movement is associated with energy.

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Concept

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Selected parameter

Calculations

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Equation

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If a body initially has an amount of heat the initial heat ($Q_i$) and subsequently has an amount of heat the final heat ($Q_f$) ($Q_f > Q_i$), heat has been transferred to the body the heat difference ($\Delta Q$). Conversely, if ($Q_f < Q_i$), the body has released heat.

$ \Delta Q = Q_f - Q_i $

Conditions

Variables

$Q_f$

Final heat

$J$

$\Delta Q$

Heat difference

$J$

$Q_i$

Initial heat

$J$

Relation

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Equation

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If a system is initially at ($$) and then is at the temperature in final state ($T_f$), the difference will be:

$ \Delta T = T_f- T_i$

Conditions

Variables

$\Delta T$

Temperature difference

$K$

$T_f$

Temperature in final state

$K$

$T_i$

Temperature in initial state

$K$

Relation

The temperature difference is independent of whether these values are in degrees Celsius or Kelvin.

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Equation

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When the variation of heat ($\Delta Q$) is added to a body, we observe a proportional increase of the temperature variation ($\Delta T$). Therefore, we can introduce a proportionality constant the heat capacity ($C$), known as heat capacity, which establishes the following relationship:

$ \Delta Q = C \Delta T $

Conditions

Variables

$C$

Heat capacity

$J/K$

$\Delta T$

Temperature variation

$K$

$\Delta Q$

Variation of heat

$J$

Relation

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Equation

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The heat capacity is related to microscopic oscillations, so it depends less on mass and more on the number of atoms. For this reason, it makes sense to introduce the concept of the specific heat ($c$), which is calculated as the heat capacity ($C$) per unit of the mass ($M$), as follows:

$ c =\displaystyle\frac{ C }{ M }$

Conditions

Variables

$C$

Heat capacity

$J/K$

$M$

Mass

$kg$

$c$

Specific heat

$J/kg K$

Relation

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Equation

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The relationship between the variation of heat ($\Delta Q$) and the variation in the temperature variation ($\Delta T$) in a solid or liquid is established by the heat capacity ($C$), according to the following equation:

By introducing the specific heat ($c$) and the mass ($M$), the equation can be expressed as follows:

$ \Delta Q = M c \Delta T$

Conditions

Variables

$M$

Mass

$kg$

$c$

Specific heat

$J/kg K$

$\Delta T$

Temperature variation

$K$

$\Delta Q$

Variation of heat

$J$

Relation

Development

The variation of heat ($\Delta Q$) is related to the temperature variation ($\Delta T$) and the heat capacity ($C$) as follows:

$ \Delta Q = C \Delta T $

Where the heat capacity ($C$) can be replaced by the specific heat ($c$) and the mass ($M$) using the following relationship:

$ c =\displaystyle\frac{ C }{ M }$

Therefore, we obtain:

$ \Delta Q = M c \Delta T$

Since specific heat does not depend on the amount of mass, its value is solely determined by the type of material. This allows for its measurement, tabulation, and subsequent reference and use.

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Equation

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The quantity of the heat capacity ($C$) in a system of the i-th mass of the system ($M_i$) with the specific heat of the i-th mass ($c_i$) can be calculated as follows:

$C = \displaystyle\sum_i c_i M_i$

Therefore, the total sum for the specific heat ($c$) calculated is:

$ c =\displaystyle\frac{ \displaystyle\sum_i c_i M_i }{ \displaystyle\sum_i M_i }$

Conditions

Variables

Relation

Development

The quantity of the heat capacity ($C$) in a system of the i-th mass of the system ($M_i$) with the specific heat of the i-th mass ($c_i$) can be calculated as follows:

$C = \displaystyle\sum_i c_i M_i$

where the sum of the masses is obtained as:

$M = \displaystyle\sum_i M_i$

So, with the help of

$ c =\displaystyle\frac{ C }{ M }$

,

we can calculate the heat capacity ($C$) as follows:

$ c =\displaystyle\frac{ \displaystyle\sum_i c_i M_i }{ \displaystyle\sum_i M_i }$

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Equation

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The specific heat of the soil depends on variables the dry mass of sand in the sample ($M_a$), the dry mass of silt in the sample ($M_i$), and the dry mass of clay in the sample ($M_c$), in addition to the mass of water in the soil ($M_w$). Together with the specific heat of sand ($c_a$), the specific heat of silt ($c_i$), the specific heat of clay ($c_c$), and the specific heat of water ($c_w$), these variables allow for the calculation of the specific heat of the soil. In particular, we can work with the proportions the mass fraction of sand in the sample ($g_a$), the mass fraction of silt in the sample ($g_i$), the mass fraction of clay in the sample ($g_c$), and the relationship gravimetric water solido ($\theta_w$) and demonstrate that:

$ c = \displaystyle\frac{ g_a c_a + g_i c_i + g_c c_c + \theta_w c_w }{1+ \theta_w }$

Conditions

Variables

Relation

Development

With the i-th mass of the system ($M_i$) and the specific heat of the i-th mass ($c_i$), you can calculate the specific heat ($c$) for the soil using the equation:

$ c =\displaystyle\frac{ \displaystyle\sum_i c_i M_i }{ \displaystyle\sum_i M_i }$

Furthermore, using the variables the dry mass of sand in the sample ($M_a$), the dry mass of silt in the sample ($M_i$), the dry mass of clay in the sample ($M_c$), and the mass of water in the soil ($M_w$) along with the specific heat of sand ($c_a$), the specific heat of silt ($c_i$), the specific heat of clay ($c_c$), and the specific heat of water ($c_w$), you can obtain the specific heat (

$c$

) with the formula:

$c=\displaystyle\frac{M_ac_a+M_ic_i+M_cc_c+M_wc_w}{M_a+M_i+M_c+M_w}$

Using the following equations:

$ g_a =\displaystyle\frac{ M_a }{ M_s }$

$ g_i =\displaystyle\frac{ M_i }{ M_s }$

$ g_c =\displaystyle\frac{ M_c }{ M_s }$

$ g_a + g_i + g_c = 1$

and

$ \theta_w =\displaystyle\frac{ M_w }{ M_s }$

Then, the specific heat ($c$) is simplified using the following equation:

$ c = \displaystyle\frac{ g_a c_a + g_i c_i + g_c c_c + \theta_w c_w }{1+ \theta_w }$

The specific heat primarily depends on the water content but also on the texture and, hence, the proportion of sand, silt, and clay in the soil. In any case, the specific heats of the different components are as follows:

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