#CONDENSE CALCULATOR HOW TO#
For example: ³√64 = 4īefore we learn how to rewrite logs, let's mention a few critical facts concerning them. However, as opposed to logarithms, roots return the exponent base, not the exponent itself (in the above language: they return how many people get infected by a single person). Note that taking a root is also considered an inverse operation to taking a power. In the above epidemic example, the logarithm (with base 4) returns at which step we get a fixed number of infected. Note, however, that in general, this can be (calc:1503). 💡 logₐ(b) gives you the power to which you'd need to raise a in order to obtain b. To make it all precise, let's see the following log definition. The logarithm is the inverse function to the exponential one. In general, we describe the number of sick in the n-th step by the exponent 4ⁿ. In turn, they got 4² = 4 * 4 = 16 people infected, who later got 4³ = 4 * 4 * 4 = 64 people infected. Indeed, if we assume that each infected person transmits the disease onto, say, 4 others, then patient zero got 4 people sick. Mathematically speaking, such a thing is called exponential growth.Īs you might have noticed, the name suggests that it has something to do with exponents. Separate calculations are thus required using Equation 1 for the material below and above the phase change temperature.With the COVID-19 pandemic raging on, there's been quite some talk about the rate at which the number of cases increases over time. The Cp value (from Equation 1) of a material also changes with a change in state. How much energy is required to melt 50 lbs of lead?Ĭhanging state (melting and vaporizing) is a constant temperature process. Hv = Latent Heat of Vaporization (Btu/ lb ) Q D = Heat Required to Melt/Vaporize Materials Processed in Working Cycle ( Wh ) Q C = Heat Required to Melt/Vaporize Materials During Heat-Up ( Wh ) This same amount of energy is released as the vapor condenses back to a liquid. The latent heat of vaporization Hv of the substance is the energy required to change a substance from a liquid to a vapor. Another state change is involved in vaporization and condensation. The heat needed to melt a material is known as the latent heat of fusion and represented by Hf. Heat Required to Melt or Vaporize a Material In considering adding heat to a substance, it is also necessary to anticipate changes in state that might occur during this heating such as melting and vaporizing. How much heat energy is needed to change the temperature of 50 lbs of copper from 10☏ to 70☏? Heated media, work being processed, vessels, racks, belts, and ventilation air should be included. This equation should be applied to all materials absorbing heat in the application. ∆T = Temperature Rise of Material ( T Final – T Initial )(☏) Q B = Heat Required to Raise Temperature of Materials Processed in Working Cycle ( Wh ) Q A = Heat Required to Raise Temperature of Materials During Heat-Up ( Wh ) Since all calculations are in watts, an additional conversion of 3.412 Btu = 1 Wh is introduced yielding:
Calling the amount of heat added Q, which will cause a change in temperature ∆T to a weight of substance W, at a specific heat of material Cp, then Q =w
The specific heat capacity of a substance is the quantity of heat needed to raise the temperature of a unit quantity of the substance by one degree. Absorbed Energy, Heat Required to Raise the Temperature of a Material Because substances all heat differently, different amounts of heat are required in making a temperature change.
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