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.