VIDEO: Calculate the mixing temperature of different substances

Basic considerations on mixing temperatures of substances

In order to calculate the mixing temperatures of different substances, you need to be clear about a few things:

• When you mix two fabrics, it all comes down to the ratio in which you mix the fabrics. It goes without saying that a drop of cold water cools hot water less than a large amount of cold water.
• It also depends on the temperature differences. Water at 80 ° C will cool boiling water less than water at 0 ° C. For the exact calculation you always have to convert the temperatures into Kelvin, because it depends on the distance to absolute zero. If you know the temperature in Celsius, add 273.15 to it and you have it in K.
• In general, mixed temperatures mean that one substance gives off energy to the other, creating a new temperature. You have to imagine that you have bound a certain thermal energy in a certain amount of substance and combine it with the thermal energy of the other amount of substance.
• Example: Thermal energy from 500 g of water at a temperature of 300 K is added to the thermal energy of 1000 g of water at a temperature of 353 K. So you have 500 g * 300 K + 1000 g * 353 K and 1500 g of water. So there is a thermal energy of 503,000 K for 1 g of water, but since you have 1500 g of water, you have to divide the value by 1500 and you get a mixed temperature of 335 K. The formula is T
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  _mix= (m₁T₁+ m₂T₂) / (m₁+ m₂).


Calculate the specific heat of ice - this is how it works

If you are dealing with thermodynamics within physics, it is interesting ...

Note: It's about the energythat is required to bring a substance to a certain temperature. The units gk, i.e. mass times temperature, is not a unit of measurement for energy. This is J. If you include the specific heat capacity c =... J / gK in the formula, it is exact. However, since this is a constant if you only mix the same substances, c can be neglected.

Calculation of mixing temperatures for different substances

If you want to calculate exactly the mixing temperature of different substances, for example because you want to calculate how much coffee cools when you have a cold one Pour milk into it, proceed from the following consideration: The mixing temperature means nothing other than that one substance cools down while the other is warmed up. These temperature changes are known as delta theta. The amount of heat that one substance absorbs is identical to the amount that the other substance gives off. Note the delta theta for fabric 1 T.₁ - T_m and for fabric 2 T₂ - T_m is.

1. Calculate the respective amounts of heat using the formula Q = c m (Delta Theta).
2. Substance 1 gives the amount of heat Q₁ = c₁ m₁ (T₁ - T_m), while the other substance is the amount Q₂ = c₂ m₂ (T₂ - T_m) records.
3. Now set Q1 = - Q2.
4. Now replace Q₁ by c₁ m₁ (T₁ - T_m) and Q₂ by c₂ m₂ (T₂ - T_m). You get equation c₁ m₁ (T₁ - T_m) = - c₂ m₂ (T₂ - T_m).
5. Solve this mathematically for T._m on. You get T_m = (c₂ m₂ T₂ + c₁ m₁ T₁) / (c₁ m₁ + c₂ m₂). the invoice is pretty easy.

The values ​​for the specific heat capacity c can be found in tables.