Constant-volume calorimeter

Calculate the heat transfer, Q, from a bomb calorimeter (constant volume) or a steady flow calorimeter (constant pressure), Qp, from theory or experimental data. 

The p V work temi is not nomially measured. It can be eliminated by suspending the calorimeter in an evacuated space (p = 0) or by holding the volume of tire calorimeter constant (dF= 0) to give... 

This is the working equation for a constant volume calorimeter. Alternatively, a calorimeter can be maintained at constant pressure p equal to the external pressure p in which case... 

Values of COT) can be derived from a constant volume calorimeter by measuring AU for small values of Tj - TO and evaluating AU/(T2 - T ) as a fiinction of temperature. The energy change AU can be derived from a knowledge of tlie amount of electrical energy required to change the temperature of the sample + container... 

Magee J W, Blanco J C and Deal R J 1998 High-temperature adiabatic calorimeter for constant-volume heat capacity of compressed gases and liquids J. Res. Natl Inst. Stand. Technol. 103 63... 

As noted earlier, for a reaction at constant pressure, such as that taking place in an open coffee-cup calorimeter, the heat flow is equal to the change in enthalpy. If a reaction is carried out at constant volume (as is the case in a sealed bomb calorimeter) and there is no mechanical or electrical work involved, no work is done. Under these conditions, with w = 0, the heat flow is equal to the change in energy, AE. Hence we have... 

In the combustion reaction as carried out in the calorimeter of Figure 7-2, the volume of the system is kept constant and pressure may change because the reaction chamber is sealed. In the laboratory experiments you have conducted, you kept the pressure constant by leaving the system open to the surroundings. In such an experiment, the volume may change. There is a small difference between these two types of measurements. The difference arises from the energy used when a system expands against the pressure of the atmosphere. In a constant volume calorimeter, there is no such expansion hence, this contribution to the reaction heat is not present. Experiments show that this difference is usually small. However, the symbol AH represents the heat effect that accompanies a chemical reaction carried out at constant pressure—the condition we usually have when the reaction occurs in an open beaker. 

FIGURE 6.12 A bomb calorimeter is used to measure heat transfers at constant volume. The sample in the central rigid container called the bomb is ignited electrically with a fuse wire. Once combustion has begun, energy released as heat spreads through the walls of the bomb into the water. The heat released is proportional to the temperature change of the entire assembly. 

We have seen that a constant-pressure calorimeter and a constant-volume bomb calorimeter measure changes in different state functions at constant volume, the heat transfer is interpreted as A U at constant pressure, it is interpreted as AH. However, it is sometimes necessary to convert the measured value of AU into AH. For example, it is easy to measure the heat released by the combustion of glucose in a bomb calorimeter, but to use that information in assessing energy changes in metabolism, which take place at constant pressure, we need the enthalpy of reaction. 

Figure 6-17 illustrates a constant-volume calorimeter of a type that is often used to measure q for combustion reactions. A sample of the substance to be burned is placed inside the sealed calorimeter in the presence of excess oxygen gas. When the sample bums, energy flows from the chemicals to the calorimeter. As in a constant-pressure calorimeter, the calorimeter is well insulated from its surroundings, so all the heat released by the chemicals is absorbed by the calorimeter. The temperature change of the calorimeter, with the calorimeter s heat capacity, gives the amount of heat released in the reaction. 

A commercial instrument for constant-volume calorimetiy is called a bomb calorimeter, because the container in which the reaction occurs resembles a bomb. 

To determine A E using measured values of q, we also must know w. Because heat and work are path functions, however, we proceed differently for constant volume than for constant pressure. To distinguish between these different paths, we use a subscript v for constant-volume calorimetry and a subscript p for constant-pressure calorimetry. This gives different expressions for the two t q)es of calorimeters ... 

As described in Section 6-1. work is the product of force and displacement. In a constant-volume calorimeter, the chemical reaction is contained within the sealed calorimeter, so there is no displacement and Wy = 0. Thus ... 

A — (jv(Constaiit — volume process) For a constant-pressure calorimeter, the volume of the reacting chemicals may change, so Wp 0 and must be evaluated. We do this in Section 6-1. 

The calculation takes more than one step, so we need to identify a process. Use Equation to find < calorimeter The heat gained by the calorimeter is supplied by the chemical reaction, so < calorimeter " calonmeter Because the calorimeter operates at constant volume, W = 0, so A " = ( reaction This energy change is for 0.1250 g of octane. Use n — mf M M to determine n, then use Equation to convert to the molar energy change A. S niolar = / n. A... 

C06-0019. In a constant-volume calorimeter, 3.56 g of solid sulfur is burned in excess oxygen gas ... 

C06-0068. Constant-volume calorimeters are sometimes calibrated by ranning a combustion reaction of known A E and measuring the change in temperature. For example, the combustion energy of... 

C06-0071. An electric heater adds 19.75 kJ of heat to a constant-volume calorimeter. The temperature of the calorimeter increases by 4.22 °C. When 1.75 g of methanol is burned in the same calorimeter, the temperature increases by 8.47 °C. Calculate the molar energy of combustion of methanol. 

The heat of combustion of solids or liquids is usually measured in a device known as an oxygen bomb calorimeter. Such a device operates at a constant volume between states 1 and 2, and its heat loss is measured by means of the temperature rise to a surrounding water-bath. This is schematically shown in Figure 2.2. The combustion volume is charged with oxygen and a special fuel is added to ensure complete combustion of the fuel to be measured. Since the process is at constant volume (V), we have... 

The simplest way to measure the change in internal energy A U is to perform a reaction in a vessel of constant volume and to look at the amount of heat evolved. We perform a reaction in a sealed vessel of constant volume called a calorimeter. In practice, we perform the reaction and look at the rise in temperature. The calorimeter is completely immersed in a large reservoir of water (see Figure 3.6) and its temperature is monitored closely before, during, and after the reaction. If we know the heat... 

AE = q, (valid with constant volume bomb calorimeter)... 

In equations 7.27 and 7.28 m(BA), m(cot), m(crbl), and m(wr) are the masses of benzoic acid sample, cotton thread fuse, platinum crucible, and platinum fuse wire initially placed inside the bomb, respectively n(02) is the amount of substance of oxygen inside the bomb n(C02) is the amount of substance of carbon dioxide formed in the reaction Am(H20) is the difference between the mass of water initially present inside the calorimeter proper and that of the standard initial calorimetric system and cy (BA), cy(Pt),cy (cot), Cy(02), and Cy(C02)are the heat capacities at constant volume of benzoic acid, platinum, cotton, oxygen, and carbon dioxide, respectively. The terms e (H20) and f(sin) represent the effective heat capacities of the two-phase systems present inside the bomb in the initial state (liquid water+water vapor) and in the final state (final bomb solution + water vapor), respectively. In the case of the combustion of compounds containing the elements C, H, O, and N, at 298.15 K, these terms are given by [44]... 

J. Coops, R. S. Jessup, K. vanNes. Calibration of Calorimeters for Reactions in a Bomb at Constant Volume. In Experimental Thermochemistry, vol. 1 R D. Rossini, Ed. Interscience New York, 1956 chapter 3. 

In your previous chemistry course, you learned about various types of calorimeters. For instance, you learned about a bomb calorimeter, which allows chemists to determine energy changes under conditions of constant volume. 

Q VSUM What properties of polystyrene make it a suitable material for a constant-pressure calorimeter Why are polystyrene coffee cups not suitable for a constant-volume calorimeter ... 

The heating value, or calorific value, expressed as kj/kg (Btu/lb), is the heat produced at constant volume bv the complete combustion of a unit quantity of coal in an oxygen-bomt calorimeter under specified conditions (ASTM D 5865-04, ASTM International, op.cit.). The result includes the latent heat of vaporization of the water in the combustion products and is called the gross heating or high heating value (HHV) Qh- And Qh in Btu/lb (x 2.326 = kJ/kjy on a dry basis can be approximated by a formula developed by the Institute of Gas Technology ... 

This highly sensitive calorimeter needs to be connected to a sensitive volumetric system in order to determine accurately the amounts of gas or vapor adsorbed. A schematic representation of the whole assembly is shown in Figure 13.4 [147]. The volumetric determination of the adsorbed amount of gas is performed in a constant-volume vessel linked to a vacuum pump. The apparatus consists of two parts the measuring section equipped with a capacitance manometer, and the vessels section that includes the cells placed in the calorimeter (a sample cell in which the adsorbent solid is set, and an empty reference cell). 

Knowing the so-called " water equivalent factor of the calorimeter, it is possible to determine the heat of combustion at constant volume with an accuracy better than 1%... 

Heat of Detonation is defined by Dunkle (Ref 40, p 248) as the "heat liberated at calorimeter temperature when an explosive detonates at constant volume and with no change in the product composition from that which was obtained at C-J point. Heat of detonation can be calculated from heat of explosion, or a closer experimental approach can be attempted by detonating the sample at high density and under strong confinement"... 

As was already mentioned, experimental determinations of heat of explosion and of heat of detonation are conducted in steel or special alloy cylindrical vessels of strong construction, known as "constant volume explosion bomb calorimeters and as "detonation calorimeters . To the brief description of such calorimeters (bombs), which is given in Vol 2 of Encycl, p Cll-R, the following may be added ... 

A common variety of constant-volume calorimetry is bomb calorimetry, a technique in which a reaction (often, a combustion reaction) is triggered within a sealed vessel called a bomb. The vessel is immersed in a water bath of known volume. The temperature of the water is measured before and after the reaction. Because the heat capacity of the water and the calorimeter are known, you can calculate heat flow from the change in temperature. 

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