Rate of increase in temperature

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

Hazardous chemical reactivity is any chemical reaction with the potential to exhibit rates of increase in temperature and/or pressure too high to be absorbed by the environment surrounding the system. Included are both reactive materials (those which enter into a chemical reaction with other stable or unstable materials) arid unstable materials (those which in a pure state or as normally produced decompose or undergo violent changes). 

By capillary action, molten fat sample is drawn into the tube, which is open at both ends. The fat is solidihed by chilling and then melted in water at a regulated rate of increase in temperature. The temperatures at which the fat shps and appears clear in the liquid state are noted as its slip/melting points or melting range. 

An equation holding between the rate of heat transfer per unit volume per unit time by the thermal conduction in a stationary medium, i.e., in a solid, in reality, and, the rate of increase in temperature of the solid is given in the following form. 

Then, according to the result of the calculation given in Table 2, at the time when the adiabatic self-heating test started from the T,. is interrupted, i.e., at the time when the temperature of the peroxide has increased by 1.25 K from the the rate of increase in temperature of the peroxide will be about 1.346 (= 1.15 X 1.1701) K/h. 

Now, as stated in Section 2.4, the T, of each run in the two kinds of adiabatic tests performed for a chemical of the TD type, including every gas-permeable oxidatively-heating substance, is selected on the basis of the self-heating property of the chemical tested to give estimated rates of increase in temperature of 1.25 K/h. 

When the rate of increase in temperature of 2 cm of the chemical subjected to the adiabatic self-heating test started from a T, has varied or has accelerated from 1.15 up to 1.346 K/h after the lapse of one hour, we may assume that the rate has remained, in fact, at a mean, and almost constant, value of 1.25 (1.15 + 1.346)/2 K/h during this one hour. 

On the other hand, when confined in the closed cell and subjected to the isothermal storage lest performed at a T, on the low temperature side, the time interval up to the start of the quasi-autocatalytic reaction occumng simultaneously with the finish of melting of 2 cm of a powdery chemical of the quasi-AC type becomes naturally far longer, and the temperature decrement caused by melting also becomes of the order of 0,1 0.2 K only. In the meantime, the rate of increase in temperature of the chemical after the start of the quasi-autocatalytic reaction also becomes so slow, as shown in Fig, 16, that it becomes somewhat uncertain to locate the point of time b on the chart of the strip-chart recorder (see Fig. 143 in Subsection 10.2.5, as an example). The same is true of the induction period of the autocatalytic reaction of a high explosive of the tnie AC type (see Fig. 125 in Subsection 9.3.5, as an example). 

In the meantime, the A Tdijf pen runs almost parallel with the time axis on the strip chart of the two-pen strip-chart recorder after the start of the adiabatic control. This denotes that the state, A - T - Tqiiii 0, IS rcslizcd. in 8.nd around 2 cm of the chemical confined in the closed cell and subjected to the adiabatic self-heating test. The A Tdiff pen, however, comes to drift toward the plus side on the strip chart in the course of time. This denotes that the state, 7 > Tam, comes to occur in and around 2 cm of the chemical confined in the closed cell, in spite of the adiabatic control, because the rate of increase in temperature, i.e., the rate of the exothermic decomposition reaction, of 2 cm of the chemical confined in the closed cell and subjected to the adiabatic self-heating test... 

Figure 40. HOect of the range of the pre-amplifier on the rate of increase in temperature, of a mixture of 50 jU L of linolic acid and 50 mg of cotton wool charged in the draft cell, into which oxygen gas is supplied at a flow rate of 2 cm7min at atmospheric pressure, and subjected to the adiabatie oxidatively-heating test started from a near 60 C, keeping ihe other conditions constant.

It has been ascertained, in result, that the rate of increase in temperature of the mixture decreases gradually at ranges above 100 yV, but the rate is kept almost constant at ranges below 50 iN (Fig. 40). Therefore, 50 /iV has been chosen as the standard range of the pre-amplifier of the recorder in the two kinds of adiabatic tests, considering Ihe stability of the adiabatic control as well. 

The rate of increase in temperature of 2 cm of BPO confined in the glass closed cell and subjected to the adiabatic self-heating test started from a 7 near... 

This time, At, is calculated at 41.2248 min by the proportional allotment. This proportional allotment may be allowable, because an almost constant rate of increase in temperature of 2 cm of TBPB charged in the open-cup cell and subjected to the adiabatic self-heating test has been realized all through this run. A value of Inzl t of 3.71904 is, hence, calculated immediately. 

The temperature of the air bath is set at a proper value, i.e., the nominal T,. of the run, by means of the temperature dial on the air bath on the basis of the selfheating property of the liquid tested to give estimated rates of increase in temperature of 1.25 K/h in the adiabatic self-heating test. It is usually a temperature 20 30 K lower than the EOT, which is measured by thermal analysis, such as DTA or DSC, of each liquid in the case of liquids tested herein, with the result that the T, ranged from 27.29 °C for THPN to 100.6 °C for DTBP. As to TBPB, the T,. ranged from 73.18 to 79.62 °C. 

In Fig. 70, Rate of increase in temperature and Radial temperature difference denote the variation of the ihermoelectroniotive force of the thermocouple 2, /.e, the variation of the r,.q,/,w , with time and the variation of the value of Trad with lime, respectively. 

A runaway reaction occurs when an exothermic system becomes uncontrollable. The reaction leads to a rapid increase in the temperature and pressure, which if not relieved can rupture the containing vessel. A runaway reaction happens because the rate of reaction and therefore the rate of heat generation increases exponentially with temperature. Alternatively, the rate of cooling increases only linearly with temperature. Once the rate of heat generation exceeds available cooling, the rate of increase in temperature becomes progressively faster. Runaway reactions nearly always result in two-phase flow reliefs. Runaway reactions are generally classified into three systems. 

For a given mass of sample, m, with specific heat capacity, s, the rate of increase in temperature, T, with time, t, is... 

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