# Resulting Temperatures when Mixing Liquids or Solids

## Calculate the final temperature when liquids or solids are mixed

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When liquids and/or solids with different temperatures are mixed together - the final mixed temperature can be calculated as

*t _{f} = (m_{1} c_{p1} t_{1} + m_{2} c_{p2} t_{2} + .... + m_{n} c_{pn} t_{n}) / (m_{1} c_{p1} + m_{2} c_{p2} + .... + m_{n} c_{pn}) (1)*

*where *

*t _{f} = final mixed temperature (^{o}C)*

*m = mass of substance (kg)*

*c _{p} = specific heat of substance (J/kg.^{o}C)*

*t = temperature of substance ( ^{o}C)*

### Example - a heated stone in a bucket of water

A granite stone of *1 kg* (specific heat *790 J/kg. ^{o}C*) is heated to

*100*and added to a bucket of

^{o}C*10 kg*water (specific heat

*4186 J/kg.*) at

^{o}C*20*. The final temperature of the water - stone "mix" can be calculated as

^{o}C*t _{f} = ((1 kg) (790 J/kg.^{o}C) (100 ^{o}C) + (10 kg) (4186 J/kg.^{o}C) (20 ^{o}C)) / (*

*(1 kg) (790 J/kg.*

^{o}C) + (10 kg) (4186 J/kg.^{o}C)*)*

* = 21.5 ^{o}C*

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