# 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.

Any comments on this?

## 1 Answer

As you say, the principle of conservation of energy states that the total energy of an isolated (aka closed) system remains constant.

Power is the rate of change of energy. So it can be deduced that the total amount of power into or out of an isolated system is zero.

Your pulverizer is not actually an isolated system. It has an input and several outputs. No energy is stored inside this system for later use, therefore all energy which comes in also goes out by one route or another.

Your question relates to the flow of energy through the pulverizer. For a continuous process in a steady state it is more logical to describe this flow in terms of power, particularly when referring to the energy consumption or output of specific machinery like a pulverizer.

• Thank you for the clear explanation, I was indeed wrong on the closed/open system definition. So under the assumption that the process is in a steady state, and using the Sankey diagram, I can state that the residual unexplained power of 4.4 kW might be due to friction or other forms of loss? – Thomas Ike Jul 31 '18 at 3:49
• Yes, the total inputs must equal the total outputs. – sammy gerbil Jul 31 '18 at 7:48