In the language running, the words heat and Température often have an equivalent direction: What a heat!

Heat in the common direction was confused a long time with the concept of temperature, because with constant pressure, it is an increasing function of the temperature: for example all the pure Substance S in the solid, liquid or gas state have a Heat-storage capacity molar with constant pressure C_P ( T ), positive. Under these conditions, as with the free air the pressure is quasi-constant P ≈ 1,013  25·10⁵ pascals, to heat a body generates a rise in its temperature. But that is not always true in particular during a change of physical status: when ice is heated, it melts with 0°C under the pressure of an atmosphere, at constant temperature. There is in this case, contribution of heat without increase in temperature.

At the 19th century, heat is comparable with a " fluide": the heating . Progress and successes of the Calorimétrie impose this theory until the end of the 19th century. This design is indeed taken again by Sadi Carnot: a thermal engine can function only if heat circulates of a body whose temperature is higher towards a body whose temperature is colder; reasoning corresponding to an analogy with a hydraulic machine which draws its energy from the drainage duct of a reserve of altitude raised towards a reserve of lower altitude.

It is only with the advent of the statistical Thermodynamique, that heat will be defined like a transfer of the thermal agitation of the particles to the level Microscopique. A system of which the particles statistically are agitated will have a temperature of balance, defined on a macroscopic scale, higher. The temperature is thus a size Macroscopique which is the statistical reflection of the kinetic energies of the particles on a microscopic scale. During random shocks, the most agitated particles transmit their kinetic energies to the least agitated particles. The assessment of these transfers of microscopic kinetic energies corresponds to the heat exchanged between systems made up of particles from which average thermal agitation is different.

The temperature is thus a intensive function of state of a thermodynamic Système definite exclusively on a macroscopic scale. On the other hand, the heat is a thermal transfer of agitation which by nature is disordered. Heat is not a function of state but a size depending on the nature of the concerned transformation.

Moreover, it is clear that the transfer can be done only in the direction of the particles statistically most agitated towards statistically the least agitated particles; i.e. that heat can pass only from the hottest system towards the coldest system. This assumption is confirmed by the Second principle of the thermodynamics which introduces the function of state Entropie.

Heat and thermodynamics

The first principle and heat

The First principle of thermodynamics is a principle of conservation of energy. It introduces the function of state of balance: U energy interns.

During a transformation of a thermodynamic System closed, the variation of energy interns U ( B ) - U ( has ) is due is with:

• the realization of a macroscopic work W ( has → B ), in general the work of the compressive forces, ∫-pdV .
• the setting concerned of a transfer of microscopic energies or heat , Q ( has → B ), at the time of the transformation.

ΔU = U (B) - U (A) = Q + W

One from of thus deduced a formal definition from heat: Q (has → B) = U (B) - U (A) - W (has → B) According to a well defined way going from has to B

If one insists on this expression defining the way, it is that the curvilinear Intégrale allowing the calculation of the work of the compressive forces ( ∫ - p.dV ), is not independent of the way followed to go from has towards B because work is not a function of state.

It also follows that heat is not a function of state and thus which it depends on the followed way.

Nevertheless under certain experimental conditions, concerned heat is equal to the variation of a function of state. It is the case for a transformation of a closed system, carried out either with constant volume: ΔU = Q_V (see energy interns), is with constant pressure: ΔH = Q_P (see Enthalpy). This property is made profitable in the Calorimétrie carried out in a Calorimètre functioning either with constant pressure or with constant volume in the case of a calorimetric Bombe.

The second principle and heat

The Second principle of thermodynamics is a principle of evolution. It introduces the function of state Entropie which is a measurement of the disorder of the matter. Any spontaneous real transformation must increase the total disorder and thus result in a phenomenon of creation of entropy . The function entropy is defined on a macroscopic scale so that its variation during the transformation of a system, corresponds to the report/ratio of the quantity of heat exchanged with the medium external on the temperature of the system:

dS = δQ_rév/T (the equality supposes here that the transformation is reversible: to see the second principle).

from where: δQ_rév = T.dS

And for a transformation finished with T constant, energy of a state (A) in a state (B) of balance:

Q_rév = T.ΔS = T. (S_B - S_A)

Heat is thus associated with the concept of entropy. The more there is creation of entropy, the more the transformation is irreversible and the weaker recovered useful work will be (see Entropie). It is what justifies the qualifier given to heat to be a degraded form of energy (see Travail and heat).

Calculation of the quantity of heat concerned at the time of a transformation affecting a pure Substance

The thermodynamic sizes of a given quantity of pure substance (N constant) depend only on two variable independent.

Two functions of state introduced by the First principle are connected to heat under certain constraints: V=cte or P=cte.

• With constant volume one chooses the function of state internal energy.

Function of state energy interns: U (T, V)

Its differential is equal to:

$dU\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; dT+\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; V\}\; \backslash \; right)\; FD\; =\; \backslash \; delta\; Q\; +\; \backslash \; delta\; W\; =\; \backslash \; delta\; Q\; -\; P.dV$

If V = cte

$dU\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_V\; dT\; =\; \backslash \; delta\; Q\_V$

the size $\backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_V$ is the Heat-storage capacity molar with constant volume, called $C\_V\; ~$ and which is expressed in J.K^-1.mol^-1 .

Heat concerned for a mole is thus equal to:

$\backslash \; delta\; Q\_V\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_V\; dT\; =\; C\_V\; dT$

For N moles

$\backslash \; delta\; Q\_V\; =\; N\; C\_V\; dT\; ~$

Finally for a transformation Isochore energy of the state defined by T_A in a state B defined by T_B $Q\_V\; =\; \backslash \; int\_\; \{T\_A\}\; ^\; \{T\_B\}\; \{nC\_V\; dT\}$

$C\_V~$ is function of T . But if the interval of T is not too large (a few tens even hundreds of degrees), one can regard it at first approximation as constant.

from where:

• With constant pressure one chooses the function of state enthalpy.

Function of state Enthalpy: H (T, P)

Its differential is equal:

$dH\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; H\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; dT\; +\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; H\}\; \{\backslash \; partial\; P\}\; \backslash \; right)\; dP\; =\; \backslash \; delta\; Q\; +\; VdP$

If P = cte

$dH\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; H\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_P\; dT\; =\; \backslash \; delta\; Q\_P$

the size $\backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; H\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_P$ is the Heat-storage capacity molar with constant pressure, called $C\_P\; ~$ and which is expressed in J.K^-1.mol^-1 .

Heat concerned for a mole is thus equal to:

$\backslash \; delta\; Q\_P\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; H\}\; \{\backslash \; partial\; T\}\; \backslash \; right)\; \_P\; dT\; =\; C\_P\; dT$

For N moles

$\backslash \; delta\; Q\_P\; =\; N\; C\_P\; dT\; ~$

Finally for a transformation Isobare energy of the state defined by T_A in a state B defined by T_B $Q\_P\; =\; \backslash \; int\_\; \{T\_A\}\; ^\; \{T\_B\}\; \{nC\_P\; dT\}$

$C\_P~$ is function of T . But if the interval of T is not too large (a few tens even hundreds of degrees), one can regard it at first approximation as constant.

from where:

• Case of the change of physical status.

Generally one considers the change of physical status carried out with the free air i.e. constant pressure (atmospheric pressure). Everyone knows that the ice melts with 0°C under the atmospheric pressure and as long as there is coexistence of the ice and liquid water, the temperature remains constant. The change of state of a pure substance is thus carried out with P = Cte and T = Cte . Concerned heat thus corresponds to a variation of Enthalpie: ΔH since the pressure is constant. It is still called Latent heat molar of change of state: L .

Temperature variation at the time of a relaxation or a compression

The infinitesimal expression of the First principle for two neighboring states can be expressed using the function energy interns U ( T , V ).

Its differential is defined by:

of the = δ Q + δ W = δ Q - P.dV

gold δ Q = C_V · dT + ℓ · FD

By definition, C_V is called the Heat-storage capacity with constant volume.

the “coefficient of latent heat of dilation”, noted ℓ, is equal according to Clapeyron to:

ℓ = P ·β· T (cf Formulas of thermodynamics ).

The differential form δ Q is thus written:

δ Q = C_V · dT + P ·β· T · FD

For a Perfect gas, β· T is worth 1, therefore the second term is not negligible whole.

If a gas brutally is slackened, it cools, and with contrario if a gas brutally is compressed, it is heated (see Compression and adiabatic pressure drop ).

Let us clarify the term “brutally”: that means that the walls of the system will not have time to transmit heat to the external medium and the transformation will be regarded as Adiabatique.

δ Q = 0

If the gas slackens, it provides work to the external medium and its internal energy decreases (reduction in the kinetic energies of thermal agitation). Thus its temperature decreases. An adiabatic pressure drop thus produces a fall of temperature in a gas, and with contrario, a compression results in an increase in temperature:

C_V · dT = - P · FD ·β· T

Relation stated by Clapeyron.

dT = - (P.T.β/C_V) . FD

At the time of a relaxation FD > 0 , therefore dT is negative.

And it is the reverse for a compression.

See too

• First principle of thermodynamics
• Transfer of heat
• Entropy
• Entropy of water
• Latent heat
• significant Heat
• Physical statistics
• Work and heat

Simple: Heat

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