Constant Pressure Calorimetry

8 Key excerpts on "Constant Pressure Calorimetry"

• 

  eBook - PDF

  Thermal Analysis

  • Bernhard Wunderlich(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  C H A P T E R 5 CALORIMETRY Calorimetry represents the effort to measure heat (caloric, see Fig. 1.1) in any of its manifestations. 1 This attempt to measure heat directly distinguishes the present discussion from Chapters 3 and 4, in which the measurement of temperature did not lead to quantitative, caloric information. There is, however, no heat meter, meaning there is no instrument which allows one to find the heat content of a system directly, as has been mentioned already in Sect. 4.1. The measurement of heat must always be made in steps and summed from a chosen initial state. The most common reference state is that of the chemical elements, stable at 298.15 Κ [Δ/ff (298) = 0; see Fig. 2.14]. 5.1 Principles and History The three common ways of measuring heat are listed at the top of Fig. 5.1. First, the change of temperature in a known system can be observed and related to the flow of heat into the system. It is also possible, using the second method, to follow a change of state, such as the melting of a known system, and determine the accompanying flow of heat from the amount of material transformed in the known system. Finally, in method three, the conversion to heat of known amounts of chemical, electrical, or mechanical energy can be used to duplicate (or compensate) the flow of heat, and thus measure heat by comparison. The prime difficulty of all calorimetric measurements is the fact that heat cannot be contained. There is no known perfect insulator for heat. During the time one performs the measurement, there are continuous losses. All calorimetry is thus beset by efforts to make corrections for heat loss. Matter always contains thermal energy, and this thermal energy is constantly exchanged. Even if there were a perfect vacuum surrounding the system under investigation, heat would be lost and gained by radiation. 219 220 Thermal Analyste PRINCIPLES AND HISTORY In calorimetry, heat measurements involve: 1.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Science of Heat and Thermophysical Studies

  A Generalized Approach to Thermal Analysis

  • Jaroslav Sestak(Author)
  • 2005(Publication Date)
  • Elsevier Science

    (Publisher)

  Chapter 12

  THERMOMETRY AND CALORIMETRY

  12.1. Heat determination by calorimetry

  Various thermometric assessments have been in the center of retailored techniques used to detect a wide variety of heat effects and properties. The traditional operation aims to measure, for example, heat capacities, total enthalpy changes, transitions and phase change heats, heats of adsorption, solution, mixing, and chemical reactions. The measured data can be used in a variety of clever ways to determine other quantities. Special role was executed by methods associated with enough adequate temperature measurements, which reveals an extensive history coming back to the first use of the word ‘calorimeter’ introduced by the work Wilcke and later used by Laplace, Lavoisier as already discussed in the previous Chapter 4 .

  Calorimetry is a direct and often the only way of obtaining the data in the area of thermal properties of materials, today especially aimed to higher temperatures. Detailed descriptions are available in various books [3 , 9 , 590 –596 ] and reviews [597 –599 ]. Although the measurements of heat changes is common to all calorimeters, they defer in how heat exchanges are actually detected, how the temperature changes during the process of making a measurement are determined, how the changes that cause heat effects to occur are initiated, what materials of construction are used, what temperature and pressure ranges of operation are employed, and so on. We are not going to describe herewith the individual peculiarities of instrumentation as we merely focus our attention to a brief methodical classification.

  If the calorimeter is viewed as a certain ‘black box’ [3] , whose input information are thermal processes and the output figures are the changes in temperature or functions derived from these changes. The result of the measurement is an integral change whose temperature dependence is complicated by the specific character of the given calorimeter and of the measuring conditions. The dependence between the studied and measured quantity is given by a set of differential equations, which are difficult to solve in the general case. For this reason, most calorimetric measurements are based on calibration. A purely mathematical solution is the domain of a few theoretical schools [3 , 594 , 596

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Chemistry

  Principles and Reactions

  • William Masterton, Cecile Hurley(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  C cal 5 51.5 kJ 10.00 8 C 5 5.15 kJ/ 8 C Knowing the heat capacity of the calorimeter, the heat flow for any reaction taking place in that calorimeter can be calculated (Example 8.3). Ignition wires heat sample Stirrer Thermometer Water in calorimeter can Insulated outer container Sample dish Steel bomb Burning sample Figure 8.5 Bomb calorimeter . The heat flow, q , for the reaction is calculated from the temperature change multiplied by the heat capacity of the calorimeter, which is determined in a preliminary experiment. Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 8-3 Enthalpy 195 ▼ 8-3 Enthalpy We have referred several times to the “heat flow for the reaction system,” symbol-ized as q reaction . At this point, you may well find this concept a bit nebulous and wonder if it could be made more concrete by relating q reaction to some property of reactants and products. This can indeed be done; the situation is particularly sim-ple for reactions taking place at constant pressure. Under that condition, the heat flow for the reaction system is equal to the difference in enthalpy ( H ) between products and reactants. The enthalpy change is designated as D H . That is, q reaction at constant pressure 5 D H 5 H products 2 H reactants Enthalpy is a type of chemical energy, sometimes referred to as “heat content.” Reactions that occur in the laboratory in an open container or in the world around us take place at a constant pressure, that of the atmosphere. For such re-actions, the equation just written is valid, making enthalpy a very useful quantity.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Thermodynamics of Natural Systems

  Theory and Applications in Geochemistry and Environmental Science

  • Greg Anderson(Author)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  This gives rise to another kind of calorimetry, cryogenic , or low-temperature calorimetry. 5.4.3 Cryogenic Calorimetry A cryogenic calorimeter ( Figure 5.5 ) is an apparatus designed for the determination of heat capacities at very low temperatures. The procedure is to cool the sample down to a temperature within a few degrees of absolute zero (a temperature of absolute zero itself Figure 5.5 A cryogenic or low-temperature calorimeter. The sample container can be raised by the rotary winch so as to be in contact with the liquid helium reservoir for cooling to 4.2 K, or lowered into the vacuum for heating. The re-entrant well in the sample container contains a heating coil. (Simplified from Robie and Hemingway (1972).) 121 5.5 The Problem Resolved (a) C P , J mol –1 K –1 C P / T (b) Figure 5.6 (a) Measured heat capacity of muscovite as a function of temperature (Robie et al. , 1976). (b) C P / T vs. T for the same data. Integration gives the shaded area under the curve, which is equal to the entropy at the upper limit of integration, in this case, S ◦ 298.15 = 287.7 J mol − 1 . is actually impossible to achieve, a fact actually implicit in the third law), introduce a known quantity of heat using an electrical heating coil, and observe the resulting increase in temperature (usually a few degrees). The quantity of heat is equal to H , and this divided by the temperature difference gives an approximate value of C P at the midpoint of the temperature range. Corrections are then made to compensate for heat leaks, for the heat absorbed by the calorimeter, and to get exact C P values from the approximate ones. The integration of C P / T values to obtain the entropy at 298.15 K is illustrated in Figure 5.6 . A much more detailed description of the calorimeter and its operation is in Robie (1987). 5.5 The Problem Resolved ...............................................................................

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Pharmaceutical Isothermal Calorimetry

  • Simon Gaisford, Michael A. A. O'Neill(Authors)
  • 2006(Publication Date)
  • CRC Press

    (Publisher)

  here. It is, however, important to know the basic designs and operating principles underpinning all modern calorimeters in order to understand the origin of calori-metric signals and to draw comparison between them. Measuring Principles There are only three methods by which heat can be experimentally measured: 1. Measurement of the power required to maintain isothermal conditions in a calorimeter, the power being supplied by an electronic temperature controller in direct contact with the calorimeter (power compensation calorimetry). 2. Measurement of a temperature change in a system which is then multiplied by an experimentally determined cell constant (adiabatic calorimetry). 3. Measurement of a temperature difference across a path of fixed thermal conductivity which is then multiplied by an experimentally determined cell constant (heat conduction calorimetry). Note that all calorimetric measurements therefore require a minimum of two experiments (one for measurement and one for calibration), although further measurements may be needed for blank corrections (such as the determi-nation of a baseline or the correction for dilution enthalpies in a titration experi-ment). A discussion of the need for, and methods of, calibration (including chemical test reactions) is the basis of Chapter 2. Power Compensation Calorimeters In power compensation calorimetry, an electrical element is used either to add heat or remove heat from the calorimetric vessel as the sample reacts, maintain-ing the sample and vessel at a given temperature. The power output from the sample is thus the inverse of the power supplied by the element. In order to be able to heat and cool, the element is usually based on the Peltier principle. A typical application of this type of calorimetry is power compensation DSC. Adiabatic Calorimetry In an ideal adiabatic calorimeter, there is no heat exchange between the calori-metric vessel and its surroundings.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Thermodynamics of Geothermal Fluids

  • Andri Stefánsson, Thomas Driesner, Pascale Bénézeth(Authors)
  • 2018(Publication Date)
  • De Gruyter

    (Publisher)

  The first reported application of flow technology to calorimetric measurements was by Priestley et al. (1965), who used an isoperibol design which measured the tem-perature difference at the outlet of the mixing chamber relative to the mean temperature of the two incom-ing liquids. His instrument was used to measure the enthalpies of formation of a series of metal complexes with EDTA. In the late 1960's, Stoesser and Gill (1967) and Monk and Wadso (1968) reported independent designs for twin-cell heat-flux calorimeters. The twin cell design uses a reference cell, identical to the mixing cell but either without flow, or with flow of the mixed liquid, to cancel non-ideal heat flux behavior. In 1969, Picker et al. published novel designs two heat-of-mixing micro-calo-rimeters. The first was an adiabatic instrument that measured the temperature increment occur-ring during the mixing process relative to the inlet temperature of the two liquids. The second design was for a flow calorimeter capable of running under adiabatic or isothermal conditions to study both liquid- and gas phase reactions. Both instruments were so sensitive that they were able to reach steady states within 1 min, so that the flow rates of the mixing fluids could be varied continuously in order to obtain heats of mixing over the entire composition range. Principles of operation for isothermal calorimeters. The underlying operating principle of isothermal calorimeters is based on heating or cooling the reaction vessel to balance the heat liberated or consumed by the mixing reaction. In order to maintain the reaction zone at a constant temperature the energy output is adjusted with a controlled heater to balance the energy arising from the chemical reaction plus the energy removed by a constant heat-leak path. The enthalpy is directly obtained from the power Af (mW) required to maintain the temperature of the calorimeter constant and the molar flow-rate f n (mol-s -1 ) of the solution.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Survival Guide to General Chemistry

  • Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  p .

  ΔE = qp − PΔV

  ΔE = ΔH − PΔV; or solving for ΔH: ΔH = ΔE + PΔV

  Enthalpy is the change in potential energy (ΔPE) of a chemical process measured as heat transfer under conditions of constant pressure; work energy change (expansion or contraction of volume) is not included. Enthalpy, however, is a useful measure of energy change for a wide variety of chemical processes and is often a close approximation of total energy change. For many chemical reactions, such as solubility reactions, reactions in solution, or reactions involving only solids and liquids, volume expansion at constant pressure is very small (ΔV ≅ 0). In these cases, enthalpy and total energy change are approximately equal: ΔE ≅ ΔH.

  Volume expansion or contraction can be significant whenever gases are formed or consumed in a reaction; the number of moles of gas then changes from reactants to products. Even in many of these cases, however, the total energy contribution from the work term (−PΔV) can often be small as compared to the enthalpy term (ΔH).

  Example:

  C 2

  H 8

  N 2

    ( I )

  +   2  

  N 2

  O

  4   ( g )

      →     3  

  N

  2  

  ( g )

  +   2   C

  O

  2  

  ( g )

  +   4  

  H 2

  O

    ( g )

  2  moles of gas     →       9  moles of gas

  At constant pressure, the work of gas expansion (w = −PΔV) equals −22 kJ/mole. (Properties of gases and energy are described in Chapter 20

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Flexible Kalina Cycle Systems

  • Tangellapalli Srinivas, N. Shankar Ganesh, R. Shankar(Authors)
  • 2019(Publication Date)
  • Apple Academic Press

    (Publisher)

  If c ν varies with temperature, one can use mean specific heat at constant volume. c ¯ υ = ∫ T 1 T 2 c v d T T 2 − T 1 (3.27) The total quantity of energy transferred during a constant volume process when the system temperature changes from T 1 to T 2 Q = m ∫ T 1 T 2 c ν d T = U 2 − U 1 (3.28) The unit for c v is kJ/kg K. The unit of molar specific heat is kJ/kmol K. 3.17  SPECIFIC HEAT AT CONSTANT PRESSURE Specific heat at constant pressure is defined as amount of heat required to raise the temperature of gas through 1°C to a unit mass at constant pressure process. c p = (d q d T) p (3.29) while the pressure is held constant. For a constant pressure process, first law of thermodynamics gives Q + U 1 = W + U 2 (3.30) Where W = P (V 2 − V 1) (3.31) therefore, Q = P (V 2 − V 1) + U 2 − U 1 = U 2 + P 2 V 2 − (U 1 + P 1 V 1) = H 2 − H 1 (3.32) since H = U + PV The specific heat at constant pressure, c p, is defined as the rate of change of enthalpy with respect. to temperature when the pressure is held constant. d H = d Q or d h = d q (3.33) ∴ c p = (d h d T) p (3.34) where h is the specific enthalpy of the system. If c p varies with temperature, one can use mean specific heat at constant pressure. c ¯ P = ∫ T 1 T 2 c p d T T 2 − T 1 (3.35) The total quantity of energy transferred during a constant pressure process when the system temperature changes from T 1 to T 2 Q = m ∫ T 1 T 2 c p d T = H 2 − H 1 (3.36) The unit for c p is kJ/kg K. The unit of molar specific heat is kJ/kmol K. 3.18  FIRST LAW APPLIED TO A POLYTROPIC PROCESS, CLOSED SYSTEM Polytropic process gives the flexibility in the representation of thermodynamic process by the generalized thermodynamic formulations. The polytropic index plays an important role in this expression as it changes from 0 to ∞, facilitates any thermodynamic process in compression region and expansion region

  Sign up to read

  Learn more about book