Originally Posted by

**Xyxyll**
It's no theory. It's the first law of thermodynamics. "The increase in the amount of energy stored in a control volume must equal the amount of energy that enters the control volume, minus the amount of energy that leaves the control volume."

This sounds remarkably similar to the equation you worded out, and that's right because it's the same! What you're missing is how the equation changes when you reach steady state.

So what happens when steady state core/pcb temperatures are reached (i.e. max temperatures)? Well, the amount of energy stored in the core and pcb (i.e. it's temperature above ambient), no longer increases. It is constant, so all future energy inputed to the system is dispersed.

Now let's try and understand how the coolers can still output the same heat, despite different temperatures.

Here's a general heat rate equation for convection: q"=hΔT, where q" is the convective heat flux, h is the convection heat transfer coefficient (determined by the cooler's materials, surface area, fan speed, shape, etc), and ΔT is the temperature difference between the card and the surrounding air.

Once steady state is reached (your 50C and 90C card example), both constant-temperature cards transfer exactly the same energy to the air (heat in = heat out). The better cooler transfers the heat with a lower temperature delta because it's h value is higher, and the poorer cooler transfers the heat with a higher temperature delta because it's h value is lower.