Bomba Calorimetro

The first law of thermodynamics tell that a change in the internal energy of a system depends on a sum of work done and the heat transferred between the system and the surroundings (1).

w=〖-P〗_ex ∆V (1)

Also, if we consider only pressure (Pext) - volume (V ) that is work done, and the volume is constant (i.e., ∆V = 0) (1,2) :

w = −Pext∆V = 0 (2)

The negative signal means that the external pressure is acting against the system that does work. If it is a reversible process, we have pressure (P) equal to Pext, so the first law at constant volume is given by: (1)

∆U = qsyst (3)

When a body is exposed to a temperature increase its enthalpy increases. In a system under constant pressure, changes in the enthalpy of the body is related to temperature by the so-called heat capacity, Cp, which is the ability of a body to store energy, illustrated in the equation:(1,2)

C_p=(∂H/∂T)_p (4)

For infinitesimal changes in the surrounding temperature in question, and considering that the heat capacity is constant in this temperature range, equation (1) can be written as:(1)

∆H=C_p ∆T (5)

Knowing that for a closed system at constant pressure and only work with pV, the change in enthalpy is given by:

∆H=q_p (6)

Replacing in Equation 2:

q_p=C_p ∆T (7)

Where the "p" subscript indicates constant pressure(1).

The heat capacity of a body depends on its mass, m, and its specific heat, c, which depends on the substances that compose it, and:(2)

C_p=m.c (8)

However, the specific heat is a function of temperature and pressure, thus the correct representation of Equation 4 would be(1):

□(24&dq_p=m∫_(T_1)^(T_2)▒〖C_p (T)□(24&dT)〗) (9)

Nevertheless, as the pressure is considered constant, this dependence is omitted, and the variation of temperature in the case of this experiment, is being considered infinitesimal. (1,2)

When two bodies at different temperatures (T1 and T2) are brought into contact, heat flows from the hotter to the cooler. The quantity of heat involved in the process is related to the ability of the bodies have to store this energy.(2)

A calorimeter allows the determination of the specific heat of a body, so in the case of the experiment, which is an adiabatic process, the changes in the temperature of the water in the bath were measured (∆T). Thus, the amount of heat produced in the combustion reaction can be calculated using the equation (7) because the heat capacity (Ccal) of, the surrounding, water is known and it is given that the specific heat of water is equal to 4.184 J / g.ºC.(2,3)

−qsyst = qsurr = Ccal∆Tsurr (10)