Rate of heat output

The thermal method consists of measuring the rate of heat output dq/dt as a function of time t in the course of a reaction. In this case, it is assumed that the quantity of heat dq is proportional to the change in the degree of conversion dp. According to this formulation, the actual nature of the reactions occurring in the material is not a concern however it is assumed that the total output Q corresponds to completion of the polymer formation process i.e., it corresponds top = 1. Therefore, the main expression for the calorimetric degree of conversion pc becomes... 

By integrating Eq. (2.50) for different cooling rates, i.e., for different functions T(t), it is possible to find the time dependence of crystallinity and the rate of the crystallization process. It is also necessary to bear in mind the temperature dependence of the equilibrium degree of crystallinity, a x (T). As an example, this dependence is shown for polycaproamide in Fig. 2.20.97 It is evident from Eq. (2.53) that the functiona(T) must have a maximum whose location on the temperature axis depends on the cooling rate. This is illustrated in Fig. 2.21, where values of the rate of heat output dQ/dt, proportional to da/dt, and degree of crystallinity a are shown as functions of temperature. It is worth mentioning that all the curves in this figure are adequately described by Eq. (2.52). 

Figure 2.21. Temperature dependencies of the rate of heat output and time dependencies of the degree of crystallinity in the homogeneously cooled polycaproamide sample. The rates of linear decrease in temperature are 2 K/min (curves 1 and 8) 4 K/min (curves 2 and 7) 8 K/min (curves 3 and 6) 16 K/min (curves 4 and 5).

Modelling of crystallization was discussed in Section 2.8. Now, we shall develop a model for superimposed polymerization and crystallization processes. This model is important for calculating temperature evolution during reactive processing, because an increase in temperature, regardless of its cause, influences the kinetics of both polymerization and crystallization. This concept is expressed by the following equation for the rate of heat output from the superimposed proceses 102,103... 

Over the last ten years, the technical development of calorimetry has reached such a stage that even very slow processes connected with a low rate of heat output, such as occur in biological systems, may be detected. A wide variety of particular designs have been used in modern biological calorimetry and applied to molecular, cellular, multicellular, and complex systems studies (general reviews by Spink Wadso, 1976 Lamprecht <5c Zotin, 1978 Beezer, 1980 Gnaiger, 1983). 

Laboratory testing showed that although the reaction between A and B was rapid at 70°C, accumulation of unreacted material would occur if the temperature was allowed to drop below 40°C. The reaction was highly exothermic with an adiabatic temperature rise of >100°C. The rate of heat output at the proposed addition rate was within the heat removal capacity of the cooling system. 

This means the rate of heat input by conduction = the rate of heat output by conduction or q is a constant with time for steady-state heat transfer. 

In the solution of heat-transfer problems, it is necessary not only to recognize the modes of heat transfer which play a role, but also to determine whether a process is Steady or Unsteady. When the rate of heat flow in a system does not vary with time-when it is constant-the temperature at any point does not change and steady-state conditions prevail. Under steady-state conditions, the rate of heat input at any point of the system must be exactly equal to the rate of heat output, and no change in internal energy can take place. The majority of engineering heat-transfer problems are concerned with steady-state systems. 

The rate of heat output (outlet stream) is given by MCp T - T )... 

High or low fuel gas pressure ean have a dramatic effect on the operation of a firetube heater. Burners are typically rated as heat output at a specified fuel pressure. A significantly lower pressure means inadequate heat release. Significantly higher pressure causes overfiring and over heating. The most common causes of a fuel gas pressure problem are the failure of a pressure regulator or an unacceptably low supply pressure. 

A breach of these emission levels is an offence under Section 2(2) of this Act. Best practicable means may be used as a fence against this action, and the Regulations prescribe to which classes of appliance they apply. Schedule 1 furnaces are rated by heat output and are boilers or indirect heating appliances where the material heated is a gas or a liquid. The maximum continuous rating concerned are from 825,000 to 475 million BTUs. 

This theory was also able to explain the energetic properties of muscle. Hill had found in 1938 that the heat produced by a muscle was proportional to the shortening distance and Huxley was able to derive this relationship from his mathematical expressions. However, Hill found later (Hill, 1964), that the rate of energy output did not increase at a constant rate as the velocity increased, as he had originally found, but declined at high velocities. This could not be explained by Huxley s 1957 theory. 

The rate of heat transfer, Q, whether it is an input or output, may be expressed as ... 

Runaway reactions can be triggered by a number of causes, but, in most cases., their resultant features after initiation are similar [31]. Whenever the heat production rate exceeds the heat removal rate in a reaction system, the temperature begins to rise and can get out of control. The runaway starts slowly but the rate of reaction accelerates, and the rate of heat release is very high at the end. Most runaways occur because of self-heating with the reaction rate (and reaction heat output) increasing exponentially with temperature, while the heat dissipation is increasing only as a linear function of the temperature. 

The rate of heat production (dQR/dt, reaction output), where applicable as a function of temperature... 

When assessing the energy output of an exothermic reaction it is advantageous to determine the rate of heat release directly, e.g., by using reaction calorimetry. Alternatively, it is possible to... 

In general, the cell energy balance states that the enthalpy flow of the reactants entering the cell will equal the enthalpy flow of the products leaving the cell plus the sum of three terms (1) the net heat generated by physical and chemical processes within the cell, (2) the dc power output from the cell, and the rate of heat loss from the cell to its surroundings. 

Determine the pump power, turbine power, net power output, rate of heat added to the heat exchanger by surface ocean warm water, rate of heat removed from the heat exchanger by deep ocean cooling water, cycle efficiency, boiler pressure, condenser pressure, mass flow rate of surface ocean warm water, and mass flow rate of deep ocean cooling water. 

An actual split-shaft Brayton cycle receives air at 14.7 psia and 70° F. The upper pressure and temperature limit of the cycle are 60 psia and 1500°F, respectively. The turbine efficiency is 85% for both turbines. The compressor efficiency is 80%. Find the temperature and pressure of all states of the cycle. The mass flow rate of air is 1 Ibm/sec. Calculate the input compressor power, the output power turbine power, rate of heat... 

Determine the total pump power input, total turbine power output, rate of heat added, rate of heat removed, cycle efficiency, and mass flow rate of ammonia. 

The answers are combined cycle—power input =—13.28 kW, power output = 988.0 kW, net power output = 974.7 kW, rate of heat added = 2994kW, rate of heat removed = —2019kW, and j = 32.56% topping steam cycle—power input = —2.02kW, power output = 898.5 kW, net power output = 896.5 kW, rate of heat added = 2994 kW, rate of heat removed = —2098 kW, and = 29.94% bottom ammonia cycle—power input= — 11.26kW, power output = 89.53 kW, net power output = 78.27 kW, rate of heat added = 2098 kW, rate of heat removed = — 2019kW, t] = 3J3%, and mass rate flow = 1.75kg/sec. (See Fig. 5.4.)... 

Determine the pressure and temperature of each state, power required by the top-cycle compressor, power produced by the top-cycle turbines, thermal efficiency of the combined cycle, thermal efficiency of the top cycle, thermal efficiency of the bottom cycle, power input to the combined cycle, power output by the combined cycle, power net output of the combined cycle, rate of heat added to the combined cycle, rate of heat removed from the combined cycle, power input to the top cycle, power output by the top cycle, power net output of the top cycle, rate of heat added to the top cycle, rate of heat removed from the top cycle, power input to the bottom cycle, power output by the bottom cycle, power net output of the bottom cycle, rate of heat added to the bottom cycle, and rate of heat removed from the bottom cycle. 

Determine the mass flow rate of the freon cycle, thermal efficiency of the combined cycle, power input to the combined cycle, power output by the combined cycle, power net output of the combined cycle, rate of heat added to the combined cycle, and rate of heat removed from the combined cycle. 

Determine the rate of heat supply, net power output, process heat output, cycle efficiency, cogeneration ratio, and energy utility factor of the cycle. 

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