Temperature multiplier

The surrounding temperature. The heat could come from nearby components or through internal heat dissipation. If we lower the temperature, the evaporation rate will decrease and extend the life. We will see a little later how this leads to the published temperature multipliers. 

Temperature multipliers These we have to be more careful about. And we have to clearly understand what they really imply. 

The datasheet usually provides certain temperature multipliers for the allowable ripple current. For example, for the old but still well-known LXF series from Chemicon, the numbers provided are... 

So what are the temperature multipliers really telling us All they really tell us is how the vendor has designed his capacitor from a thermal point of view, or what exactly is the capacitor s core temperature. As we will see, if we stick to the RMS current rating of the capacitor (without applying temperature multipliers), we don t really need to know the details of the core temperature either. Temperature multipliers were therefore just objects of abuse by some designers in the past. This is perhaps why nowadays most elko datasheets are no longer even carrying that information. 

So the multiplier must be 5°5 = 2.236, which agrees with the published datasheet value. Therefore we see that from the vendor s published ripple current temperature multipliers, we can easily deduce his designed-in maximum core temperature. 

The problem with this is that if the core temperature is at its maximum rated 115°C, the life would always just be the declared 2000 hours or so. That is hardly enough to get us through even one quarter of a year. We usually need at least about 44,000 hours (5 years) of life expectancy from all elkos used in a typical commercial power supply. So how do we get there We do that by reducing the core temperature, thereby slowing down the evaporation rate of the electrolyte. Does this imply we should not be using temperature multipliers to increase the current Yes, in fact it does. 

There is actually another complication. It has been determined that not only is the absolute value of the core temperature important, but the differential from can to core is critical too. So if we increase the differential beyond the designed-in 5°C, the life can deteriorate severely, even if the can itself is held at a much lower temperature. But the designed-in differential of 5°C occurs ONLY when we pass the maximum specified ripple current (no temperature multipliers applied), irrespective of the ambient. Which means that as a matter of fact we cannot use any temperature multipliers at all. So, if the capacitor is rated to pass 1A at 105°C, then even at an ambient of, say, 65 °C, we are allowed to pass only 1A, not 2.23A. 

We see that we cannot have our cake and eat it too. We can increase the ripple current (but degrading its life) by applying the temperature multipliers. Or we can increase the life (but not the ripple current) by not applying these multipliers. We just can t have it both ways ... 

Question If we pass the rated ripple current through a 2000 hour capacitor (no temperature multipliers applied) at an ambient of 55°C, what is the expected life (first pass estimate) ... 

Capacitor manufacturers recommend that in general we don t pass any more current than the maximum rated ripple current. This ripple current is the one specified at the worst case ambient (e.g., 105°C). Even at lower temperatures we should not exceed this current rating. No temperature multipliers should be used. Because only then is the case to core temperature differential within the design specifications of the part. And only then are we allowed to apply the simple 10°C doubling rule for life. 

Determining the conversion of monomer can only be as accurate as the method of quantifying the heat liberated from the reaction. The usual method is to take the difference between the inlet and outlet jacket water temperatures multiplied by the specific heat and flow rate of the water. This steady-state energy balance equation is ... 

With no heat being transferred through the jacket, an accurate prediction of the jacket water outlet temperature should be possible by knowing the history of the jacket inlet temperature and the mixing characteristics of the jacket. Therefore, the difference between the actual and predicted outlet temperatures multiplied by the flow rate and specific heat of the water should also equal Q. 

Young found from van der Waals s equation that the ratio of the actual density at the critical point to the theoretical density for the ideal gas should be (8/3)- /2=3 77 for all substances. The actual values are not far from this, except for alcohols and acetic acid, which have values of 4 to nearly 5. The density of saturated vapour is equal to the ideal gas density at the same corresponding temperature multiplied by a constant k ... 

Step 1. Set initial values of parameters. Let Tj be the initial temperature, 7 the final temperature, g the temperature multiplier, N the desired number of Metropolis iterations, IGM the counting number of a Metropolis iteration and / the counting number of a sample... 

The partial vapour pressure of A in a solution, at a given temperature, is equal to the vapour pressure of pure A, at the same temperature, multiplied by the mole fraction of A in the solution. 

An optimal result for AR-IHC is correlated with the mathematical product of the heating temperature multiplied by the time of AR heating treatment T (temperature of heating AR procedure) x t (period of heating time). 

So what is the actual story the temperature multipliers are telling us The amount of heating and the core temperature rise are proportional to l MS, so if we assume that in every case the final core temperature was the same, that is, Tcore - then comparing the 105°C ambient case with that at 85 °C ... 

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