Thermal lag

The proportionality constant g includes such parameters as the number of thermoelectric couples in the pile, their thermoelectric power, and the gain of the amplification device. It is supposed, moreover, that the response of the recording line is considerably faster than the thermal lag in the calorimeter. The Tian equation may also be written therefore ... 

This simplified equation is equivalent to Tian s equation [Eq. (16)], and it appears that n is indeed the time constant r of the calorimeter. Thence, the successive coefficients n in Eq. (29) may be called the calorimeter time constants of 1st, 2nd,. .., ith order. When the Tian equation applies correctly, all time constants r, except the first r may be neglected. Since the value of the coefficients n of successive order decreases sharply [the following values, for instance, have been reported (40) n = 144 sec, r2 = 38.5 sec, r3 = 8.6 sec, ri 1 sec], this approximation is often valid, and the linear transformation of many thermal phenomena produced by the thermal lag in the calorimeter may actually be represented correctly by Eqs. (16) or (30). It has already been shown (Section IV.A) that the total heat produced in the calorimeter cell is then proportional to the area limited by the thermogram. 

Some early calorimeters use thermal methods based on principles of heat and mass balance (12) and temperature rise of a constant flow of air through the combustion chamber (13). These calorimeters suffer from many drawbacks associated with their design. Heat and mass balance requires numerous measurements to account for all heat and mass flows. In most cases, thermal lag and losses in the equipment occur, which are not easily calculated. 

The front panel control varies the duty cycle, the time the controller is full on, to the time the controller is full off. If the flask, contents, and heating mantle are substantial, it takes a long time for them to warm up and cool down. A setup like that would have a large thermal lag. With small setups (approx. 50 ml. or so), there is a small thermal lag and very wild temperature fluctuations can occur. Also, operating a heating mantle this way is just like repeatedly plugging and unplugging it directly into the wall socket. There are not many devices that easily take that kind of treatment. 

H. M. Heuvel, K. C. J. B. Lind. ComputerizedAnalysis and Correction of Differential Scanning Calorimetric Data for Effects Due to Thermal Lag and Heat Capacity Changes. Anal. Chem. 1970, 42, 1044—1048. 

Our examples above demonstrated this quantitatively. For this reason, it is vital to design a reactor control system with very fast measurement dynamics and very fast heat-removal dynamics. If the thermal lags in the temperature sensor and in the cooling jacket are not small, it may not be possible to stabilize the reactor with feedback control. 

The Sir Galahad has been found to provide rapid, rehahle analysis, often in minutes, while other techniques rely on a long sample-collection timescale. Recent developments in the choice of adsorber have provided additional benefits, mainly related to reduced back pressure and less thermal lag. These allow the analyses to be completed in shorter timescales. 

The accuracy with which the differential heats of adsorption could be measured is ca. 2%. Rapid collection of evolved heat is an important criterion and sometimes, the calorimeter response has to be corrected from the instrumental distortion due to thermal lags. The peak width at half maximum of the signal from the thermal fluxmeters allows comparing the various calorimeters responses [62]. 

Figure 15.8 Thermal conductivity bridge electronic circuit. 12 V dc power supply, stable to 1 mV. Ripple is not significant due to thermal lag of the filaments. Pj, 100 ohms for filament current control Mj, milliamp meter, 0-250 mA P2, 2 ohms for coarse zero. Filaments 1 and 4 are detector 1 2 and 3 are detector 2. P3,1 ohm for fine zero Ri j, R12, padding resistors 64 ohms Rj-Rio, attenuator resistors 1, 2, 4. .. 512 ohms Si (DPDT) switch for polarity. Attenuator resistors are 0.25 %w/w, lowest temperature coefficient all others are 1 %.

As the thickness of the laminate increases, the strength of this thermal spike and the degree of thermal lag during heat-up increases. Figure 8.8 shows the results for a 62.5-mm (500 ply) laminate of the same material. Now the center-line temperature never reaches the autoclave temperature during the first dwell, and the thermal spike during the second dwell is nearly 135°C. The thermal spike is directly related to the release of internal heat during cure. The thermal lag is a manifestation of the low thermal diffusivity of polymer matrix composites. 

Figure 15.4 The large thermal lag between the part (PARTTC) and autoclave (AIRTC) is not linear or a constant. This cure cycle, however, was written for the autoclave temperature. Pressure is applied at minimum viscosity and compaction is good with few voids...

The cell is enclosed in a thermostat bath but thermocouples are placed in the cell interior to measure the thermal lag between the cell and the bath. 

The variation of apparent T with DSC heating rate has generally been attributed to the thermal lag of the sample, which increases in step with the heating rate (20-221. This thermal lag is composed of a machine path error and a sample error which are dependent on the characteristics of the instrument and the sample, respectively (211. However, T itself is a rate dependent parameter, and a dependence on scan rate involving a relaxation activation energy is to be anticipated over and above any thermal lag errors. 

Rate of heating this is very important if you intend to repeat the experiment on a subsequent occasion. Obviously the rate of heating of the sample in the crucible is not instantaneous but depends upon conduction, convection and radiation within the system. Thermal lag is therefore likely to be observed. 

Equation (95) cannot be used to analyze the thermokinetics of processes that are accompanied by fast heat evolutions because the thermal response of a heat-flow calorimeter (the thermogram) is deformed by thermal lags. In this case a more complicated analysis 34, 32) is necessary but is rarely used, and we shall not discuss it here. In its place some authors use a semiquantitative... 

More complex thermal lag effects Not as precise linear heating rate Many experimental parameters... 

Since there is no contact between pan and furnace, the thermal lag is higher than in DSC. The standards recommended by ICTA and distributed by NBS are ferromagnetic standards exhibiting loss of ferromagnetism at their curie point temperature within a magnetic field Nickel (354°C), Permanorm 3 (266°C),... 

The temperature of each point T is the sample temperature, not the programmed temperature. Due to the thermal lag, a correction depending on the instrument has to be done for each point. 

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