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# 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

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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Temperature

oC
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

kgf
N
lbf

Velocity

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

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

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