MadSci Network: Engineering
Query:

Re: A question in regards to the second law of thermodynamics.

Date: Tue Apr 8 06:18:47 2008
Posted By: Dr. James Kranz, Research Scientist
Area of science: Engineering
ID: 1206283039.Eg
Message:

Dear Shawn,

Thanks for your question. If I understand it correctly, you�re curious about net energy efficiency, either in powering a motor from a battery or in the power necessary to fully charge a battery. You also have a hunch that the second law of thermodynamics is important in understanding this process.

Since my expertise is in thermodynamics (energy balance) rather than specifically in batteries, let�s start with a discussion of energetics. There have been other questions posted to the MadSci Network that deal with energy efficiency and the laws of thermodynamics that you might be interested in reading:

Re: why is some energy put into engine not converted to work?

Paraphrasing from that posting, the three laws of thermodynamics simply state that (1) energy is conserved, (2) entropy always increases, and (3) entropy goes to zero at the limit of absolute zero temperature. Entropy is one aspect of thermodynamic description of energy that deals with disorder and randomness, which we observe to always be greater than zero. Put another way, no energetic process is every completely efficient or reversible once all sources of energy are accounted for. Essentially, for a system with an engine run by a battery, the first law means that you'll always need a battery as big as the engine (110 V for each), the second law means that we can not expect to get 100% efficiency in energy transfer (thus a 120 V battery for a 110V load), and the third law means that the closer we get to absolute zero (-273�C or -460�F) the less losses we'll incur in powering the motor. Unfortunately, the reason the entropic cost or penalty of our system goes away at absolute zero is because all energetic processes go to zero at absolute zero.

We should understand a little more about how batteries store and discharge energy to really get a sense of where our inefficiencies may lie. The voltage of a battery is a fundamental characteristic of a battery, which is determined by the chemical reactions in the battery, the concentrations of the battery components, and the polarization of the battery. Since the electric potential (voltage) from most chemical reactions is on the order of 2V while the voltage required by loads is typically larger, in most batteries, numerous individual battery cells are connected in series. For example, in lead-acid batteries, each cell has a voltage of about 2V. Six cells are connected to form a typical 12V lead-acid battery. Battery discharge and charging power is not constant, both fluctuating and diminishing over the time of its use. Lead-acid batteries are notoriously poor in their loss of voltage over time, while nickel-cadmium batteries have a long period of time over which they deliver a constant voltage.

For a battery/motor system, the energy of the system can be parsed into a work energy, general heat loss, and a battery efficiency, which can be further divided into the coulombic efficiency and the voltage efficiency. The coulombic efficiency of battery the ratio of the number of charges that enter the battery during charging compared to the number that can be extracted from the battery during discharging. The losses that reduce coulombic efficiency are primarily due to the loss in charge due to secondary reaction, such as the electrolysis of water or other redox reactions in the battery. In general, the coulombic efficiency may be high, in excess of 95%. The voltage efficiency is determined largely be the voltage difference between the charging voltage and voltage of the battery during discharging. The dependence of the battery voltage on BSOC (Battery State Of Charge) will therefore impact voltage efficiency.

Practically speaking, the peak power demand of the motor must be below the minimum discharge voltage of the battery if you don't want the motor to cut out during operation.

For more on the subject, I would invite you to review an introductory Chemistry textbook, in particular on the chemistry of Red-ox (Reduction/Oxidation) reactions, and perhaps as well a course in physical chemistry.

I hope this helps.

Regards,
Dr. James Kranz


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