 # cooling, copper or aluminum

Sometimes the question comes up, whether to use copper or aluminum for cooling purposes. Two figures are generally important, the heat conductivity and the heat capacity.

## Copper

Copper has
• an atomic weight of 63.5g / mol
• a density of 8920kg / m^3
• a molar volume of 7.11 cm^3
• a thermal conductivity of 400W / m*K
• an expansion coefficient of 16.5 *10^-6 / K
• a heat capacity of 24 J / K*mol

## Aluminum

Aluminum has
• an atomic weight of 27.0g /mol
• a density of 2700kg / m^3
• a molar volume of 10.0 cm^3
• a thermal conductivity of 235W / m*K
• an expansion coefficient of 23.1 *10^-6 / K
• a heat capacity of 24 J / K*mol

## Calculated conclusions

From the above values follows for the weight
• copper has a heat capacity of 0.378 J / K*g
• aluminum has a heat capacity of 0.888 J / K*g
• copper has only 42% of the capacity per weight { 0.426 }
• aluminum has 2.35 fold the capacity per weight { 2.35 }
for the volume
• copper has a heat capacity of 3.37 J / K*cm^3
• aluminum has a heat capacity of 2.40 J / K*cm^3
• copper has 40% more capacity per volume { 1.40 }
• aluminum has 29% less capacity per volume { 0.712 }

## Compensate the conductivity

Now let us increase the crossection for aluminum to
compensate the lesser conductivity.
• copper has a conductivity that is 70% better { 1.70 }
• aluminum has a conductivity that is 59% of the copper one {0.587 }
Thus we take 70% more aluminum and get the
• weight advantage on capacity of aluminum is down to 38% better than copper { 1.38 }
• volume advantage on capacity of copper is increased to 2.38 fold against aluminum { 2.38 }
for a unit length of equally good conduction
So when heat has to be dumped, the more the better, the quicker
the better, the results are :
If weight or cost is a concern, aluminum is favoured,
if volume is a concern, copper is better.

## The system should be fast

The application may require a good head conduction with lowest heat
capacity, for example when a dynamic systems should behave as fast
as possible. Thus let us now get the conduction to capacity ratio.
Related to weight we get for
• aluminum 267 W*g / m*J
• copper 1058 W*g / m*J
Related to volume we get for
• aluminum 80 W*cm^3 / m*J
• copper 119 W*cm^3 / m*J
Here, in both cases copper is better suited for a fast system.

To be continued...