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Mixing Liquids and/or Solids - Final Temperatures

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

tf = (m1 cp1 t1 + m2 cp2 t2 + .... + mn cpn tn) / (m1 cp1 + m2 cp2 + .... + mn cpn)                               (1)

where

tf = final mixed temperature (oC)

m = mass of substance (kg)

cp = specific heat of substance (J/kgoC)

t = temperature of substance (oC)

Example - a heated stone in a bucket of water

A granite stone of 1 kg (specific heat 790 J/kg.oC) is heated to 100 oC and added to a bucket of 10 kg water (specific heat 4186 J/kgoC) at 20 oC. The final temperature of the water - stone "mix" can be calculated as

tf = ((1 kg) (790 J/kgoC) (100 oC) + (10 kg) (4186 J/kgoC) (20 oC)) / ((1 kg) (790 J/kgoC) + (10 kg) (4186 J/kgoC))

   = 21.5 oC

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.

m1 - mass (kg)

cp1specific heat of substance (J/kgoC)

t1 - temperature (oC)

m2 - mass (kg)

cp2specific heat of substance (J/kgoC)

t2 - temperature (oC)


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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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