Temperature mixing formula

This page is to help calculating the amount of one liquid you need to add to another to get a special temperature. This is often usefull if you perform a temperature shift for example with cultures of organisms that carry a temperature sensitive mutant.

Formula

Here is a form of Richmann’s calorimetric mixing formula:

[math]\displaystyle{ m_{1}= \frac{m_{2}\cdot T_{2}- T_{m}\cdot m_{2}}{T_{m}-T_{1}} }[/math]

• m₁ is the mass of the liquid you want to add
• m₂ is the mass of the liquid that you have
• T₁ is the temperature of the liquid you want to add
• T₂ is the temperature of the liquid you have
• T_m is the temperature that you want to have after mixing

Example

Suppose you have a 100 ml culture at 39°C and want to shift it to 30°C with the help of 4°C cold fresh medium.

• m₂=100
• T₁=4
• T₂=39
• T_m=30

Than the formula is:

[math]\displaystyle{ m_{1}= \frac{100\cdot 39- 30\cdot 100}{30-4} }[/math]

That means that m₁ is 34.6, so if you add 34.6 ml of 4°C cold fresh medium to your culture it will be 30°C warm.

Please note that the described formula describes how it would be in theory. In reality for example the heat of the flask you use will also contribute and if you need very exact temperatures you would want to try with water first to see what you get.