Heat capacity, 33 Isolated system

Fig. 18. Heat capacity of a cooperative system as a function of the excess energy on aggregation. The critical temperature of a First order transition is reached with the last curve (parameter = 454). The parameter 0 corresponds to an isolated hindered rotator. Curves after data of Ref.ll0b)...

To measure the heat flow in a process, you need an isolated system, like a Thermos . An isolated system stops matter and energy from flowing in or out of the system. You also need a known amount of a substance, usually water. The water absorbs the heat that is produced by the process, or it releases heat if the process is endothermic. To determine the heat flow, you can measure the temperature change of the water. With its large specific heat capacity (4.184 J/ g-°C) and its broad temperature range (0°C to 100°C), liquid water can absorb and release a lot of energy. 

Suppose next that the heat exchange is allowed to be so extensive as to effect a temperature change in each reservoir and the process is allowed to continue until both components have reached an equilibrium temperature Tf. Let and C2 be the heat capacity of each region, and for simplicity assume these quantities to be independent of temperature. Then, if the overall system is isolated,... 

An average man weighs about 70 kg and produces about 2500 kcal of heat per day. (a) Suppose that a man were an-isolated system and that his heat capacity is... 

A simpler device than the constant-volume calorimeter is the constant-pressure calorimeter, which is used to determine the heat changes for noncombustion reactions. A crude constant-pressure calorimeter can be constructed from two Styrofoam coffee cups, as shown in Figure 6.9. This device measures the heat effects of a variety of reactions, such as acid-base neutralization, as well as the heat of solution and heat of dilution. Because the pressure is constant, the heat change for the process is equal to the enthalpy change MI). As in the case of a constant-volume calorimeter, we treat the calorimeter as an isolated system. Furthermore, we neglect the small heat capacity of the coffee cups in our calculations. Table 6.3 lists some reactions that have been studied with the constant-pressure calorimeter. 

So far, all we know about entropy is that it increases in spontaneous reactions in isolated systems, and that it appears in equations such as (4.55) and (4.56). Hidden in the equations we have derived so far is an important relationship between entropy and heat capacity, which we will see in Chapter 5 serves as a basis for the measurement of entropy. 

EXAMPLE 8.6 The equilibrium temperature of objects in thermal contact. Suppose objects A and B have different constant-volume heat capacities, Ca and Cb, both independent of temperature. Initially, object A is colder with temperature Ta, and object B is hotter with temperature Tb- A and B are brought into thermal contact with each other, but they are isolated from the surroundings. At equilibrium, Example 7.2 shows that both objects will have the same temperature T. What is the final temperature Because the objects are isolated from the surroundings, there is no net change in the energy of the total system ... 

The random motion of molecules causes all thermodynamic quantities such as temperature, concentration and partial molar volume to fluctuate. In addition, due to its interaction with the exterior, the state of a system is subject to constant perturbations. The state of equilibrium must remain stable in the face of all fluctuations and perturbations. In this chapter we shall develop a theory of stability for isolated systems in which the total energy U, volume V and mole numbers Nk are constant. The stability of the equilibrium state leads us to conclude that certain physical quantities, such as heat capacities, have a definite sign. This will be an introduction to the theory of stability as was developed by Gibbs. Chapter 13 contains some elementary applications of this stability theory. In Chapter 14, we shall present a more general theory of stability and fluctuations based on the entropy production associated with a fluctuation. The more general theory is applicable to a wide range of systems, including nonequilibrium systems. 

Feedwater system pipe break High design pressure SGs, piping, and isolation valves. Integral RV has large primary water heat capacity. Reduced probability, reduced consequences (no high pressure relief from reactor coolant system)... 

A typical human produces about 10 MJ of energy transferred as heat each day through metabolic activity, (a) If a human body were an isolated system of mass 65 kg with the heat capacity of water, what temperature rise would the body experience (b) Human bodies... 

Adopting the large capacity main steam isolation valve (MSIV) reduces the number of main steam (MS) lines and the number of MSIVs. The number of residual heat removal (RHR) systems is reduced to one line by substituting a clean up water system (CUW) for an RHR because of the use of the large capacity CUW heat exchanger adopted in large capacity BWRs. 

If an exothermic reaction takes place in an isolated system, in other words, when the heat exchange with environment is absent (adiabatic reactor), a temperature will apparently increase over time. The rate of this increase depends both on the kinetic parameters (rate constant) and on the thermodynamic properties of the system (thermal conditions of the reaction, heat capacity). For a well-mixed periodic reactor, where a single first-order reaction A —> B occurs, the mathematical model is described by this set of equations ... 

In addition to assuming that the calorimeter is an isolated system, assume that all there is in the system to absorb heat is 50.00 mL of water. This assumption ignores the fact that 0.0625 mol each of NaCl and H2O are formed in the reaction, that the density of the resulting NaCl(aq) is not exactly 1.00 g/mL, and that its specific heat capacity is not exactly 4.18 J g Also, ignore the small heat capacity of the Styrofoam cup itself. 

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