# Mixing Liquids and/or Solids - Final Temperatures

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

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*

### Mixed Temperature Calculator

The calculator below is based on eq. 1 and can be used to calculate the final - strike - temperature when two liquids or solids - or a liquid and a solid - is mixed together.

* m _{1} - mass (kg)*

* c _{p1} - specific heat of substance (J/kg^{o}C)*

* t _{1} - temperature (^{o}C)*

* m _{2} - mass (kg)*

* c _{p2} - specific heat of substance (J/kg^{o}C)*

* t _{2} - temperature (^{o}C)*

### Mixing Liquids and/or Solids - Final Temperatures Spreadsheet Calculation

The Google Docs spreadsheet below can be used to calculate final temperature when mixing fluids or solids. You can copy or download the spreadsheet to make your own copy.

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