Mixing Liquids and/or Solids - Final Temperatures

When 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 "mix" 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

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)

c_p1 - specific heat of substance (J/kg^oC)

t₁ - temperature (^oC)

m₂ - mass (kg)

c_p2 - specific heat of substance (J/kg^oC)

t₂ - temperature (^oC)

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.

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

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm