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The calorimetry is the part of the Thermodynamique which has as an aim the measurement of the quantities of heat. One uses for that a Calorimètre. This one can function either with constant pressure and in this case heats concerned within the calorimeter are equal to a variation of Enthalpie ΔH = QP , or with constant volume in a calorimetric Bombe and in this case concerned heats are equal to a variation of the internal energy ΔU = QV .

Heat not being a function of state, the quantity of heat concerned during a transformation depends on the way of proceeding (transformation Réversible or Irréversible). This is why it is necessary that the quantity of heat is equal to the variation of a function of state, which is the case with constant pressure or constant volume.

Basic principle

The calorimeter is a isolated thermodynamic Système which exchanges any energy with the external medium (neither work, nor heat). Its wall is indeformable and Adiabatique. Thus W = 0 and Q = 0 .

Nevertheless there are transfers of heat between the various parts of the calorimeter: components studied, additional, wall…. As there is no heat transfer with outside, that implies that the sum of exchanged heats Qi within the calorimeter is null: ∑ Qi = 0 .

Example of comprehension: determination of the temperature of balance of a mixture of components introduced at various temperatures

Let us consider a calorimetric system made up of I bodies defined by their mass mi, them Heat-storage capacity Ci and their initial temperature before ti mixture. Heat concerned by each body to reach the balance of temperature te, if there is no Changement of state nor of Chemical reaction, is given by the relation:

  • Q_i = m_iC_i (t_e - t_i) ~

Let us apply the relation of calorimetry ∑ Qi = 0 .

One obtains:

  • \ Sigma m_iC_i (t_e - t_i) = 0~

and thus:

t_e = \ frac {\ Sigma m_iC_i t_i} {\ Sigma m_iC_i}

Note: in this example one did not take account of the heat-storage capacity of the calorimeter.

Determination of a heat of change of state: mix water, ice with constant pressure

If a change of state occurs, one can determine by calorimetry the heat of change of state L.

One introduces a piece of ice of mass m1 , of heat-storage capacity C1 at the temperature t1 < 0 (in °C) in a calorimeter containing a liquid water mass m2 of capacity C2 and at the temperature t2 > 0 . The final temperature of balance is te > 0 .

Which are heats concerned in the calorimeter?

  • Heat to raise the temperature of the ice of t1 with 0°C: Q1 = m1C1 (0 - t1) .
  • Fusion heat of the ice with 0°C: Q2 = m1Lf .
  • Heat to raise the temperature of water coming from the fusion of the ice of 0 with te°C: Q3 = m1C2 (te - 0) .
  • Waste heat by water with t2°C: Q4 = m2C2 (te - t2) .

Let us apply the relation of calorimetry then: ∑ Qi = 0 .

Q1 + Q2 + Q3 + Q4 = 0 .

One from of deduced the equation:

m_1 C_1 (0 - t_1) + m_1L_f + m_1C_2 (t_e- 0) + m_2 C_2 (t_e - t_2) = 0 \,

The measurement of te , makes it possible to determine the fusion heat of the ice L (were) .

Approximations : One neglected here the heat-storage capacity of the calorimeter and one considered that the heat-storage capacities of water and the ice were constant whereas actually they depend on T. Specify moreover that the heat-storage capacities are here given with constant pressure: CP.

Determination of a heat of combustion to constant volume

The determination of heats of combustion is very important in the industry of fuels because it allows measurement them calorific value. One proceeds in a calorimetric Bombe. One introduces m1 G of fuel into the bomb filled with sufficient oxygen under pressure so that combustion is complete. The bomb is immersed in a calorimeter containing a great quantity of water Mg of heat-storage capacity C (water) ; the heat-storage capacity of the calorimetric unit (+ calorimeter bends) is C (cal) . That is to say ti the initial temperature. One starts the reaction by a fusing. The temperature of the calorimeter increases and is stabilized with te .

Let us call Q (comb) the heat released by the reaction. This heat is absorbed by the calorimetric unit and the products of the reaction present in the bomb. One neglects the influence of these products in front of the high mass of the calorimeter and the water which it contains.

The relation of calorimetry makes it possible to write: ∑ Qi = 0 .

Q (comb) + (M*C (water) + C (cal)) (t_e - t_i) = 0 \,

The heat-storage capacities are here given with constant volume: CV. The solution of this equation makes it possible to determine Q (comb) for m1 G of product. This heat is concerned at constant volume Qv and corresponds to a variation of the internal energy of the reactional system. It then makes it possible to calculate heat with constant pressure Qp correspondent with a variation of Enthalpie, thanks to the approximate relation:

  • Qp ≈ Qv + Δn (gas) RT

    • Δn (gas) is the variation of the number of moles of gas during the reaction of combustion.
    • R is the constant of the Perfect gas.
    • T is the temperature expressed in Kelvin.

In general a fuel is used with the constant atmospheric pressure. It is thus useful to know the heat of combustion Qp which it is possible to determine thanks to the calorimetric bomb.

Internal bonds

External bonds

  • microcalorimetry is under development strong to characterize the heat transfers during reaction in microbiology.

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