Temperature in Mixed Liquids or Solids

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

t_f = (m₁ c_p1 t₁ + m₂ c_p2 t₂ + .... + m_n c_pn t_n) / (m₁ c_p1 + m₂ c_p2 + .... + m_n c_pn)       (1)

where

t_f = final mixed temperature (^oC)

m = mass of substance (kg)

c_p = 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 mixture can be calculated as

t_f = ((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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Related Topics

• Thermodynamics - The effects of work, heat and energy on a system

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