# Is the first law of thermodynamics (conservation of energy) also applicable to power?

I am familiar with the first law of thermodynamics which states that the total energy [J] of an isolated system remains constant. Based on this law one can, for instance, create a Sankey diagram of a system that represents how the energy transforms from one form into another like this example I found online:

Now I was wondering if this law of conservation also applies for Power [J/s] in a system. For my research, I deduced how the power flow goes for a grinding machine (closed system): from engine input power to three other forms (Grinding Energy, Heat Production and Power Loss).

Fyi: The grinder (pulveriser) works based on 3 beater plates rotating at high speeds to crack inflowing material upon impact. Apart form breaking the material, the extreme speeds at which these plates rotate also create a tremendous amount of turbulence in the grinding chamber, resulting in heat generation.

The resulting Sankey diagram for the grinder running at constant speeds looks like this:

I was able to mathematically calculate the Grinding Power (1) and Heat Production (2, 3) but for the Power Loss (4, 5) I applied the law for conservation of energy to explain the last 4.4 kW as power loss due to friction in the system (no.4).

Intuitively I would say that this way of deduction is correct, but for some reason I am not 100% sure if the law of conservation of energy directly relates to power as well. Unfortunately, I cannot find literature on the conservation of power.