Resulting Temperature when Mixing Liquids or Solids

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

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/kg.oC)

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/kg.oC) at 20 oC. The final temperature of the water - stone "mix" can be calculated as

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

   = 21.5 oC

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