While holding an object, no work done but costs energy (in response to a similar question)

I read the answer to Why does holding something up cost energy while no work is being done?

and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of referring to muscle cells and biophysics, he answered my question in terms of entropy. He told me that while my arm muscles are stretched when I hold the object, they are more ordered. When my arm is at rest and muscles are not contracted, the muscles are less ordered (more entropy). So his conclusion was that the energy is required to keep the system (my arm muscles) from going to a state of higher entropy.

However, the answer in terms of muscle cells doing work on each other (i.e the answer to the hyper-linked question) made more sense to me. Could someone please give me some intuitive sense to my teacher's answer or explain the link between the two answers if there are any...

Your teacher's explanation is incorrect. A simple counterexample can be constructed to illustrate this by considering what happens when the role of your arm is replaced by that of a rubber band.

When a weight is suspended from the ceiling by a rubber band, the band stretches and its polymer chains become more ordered, in exact analogy to your teachers claim for an arm holding a weight. However, the rubber band can suspend the weight indefinitely for as long as you leave it there, and it's obvious that no energy is expended during that time.

The correct answer, as you alluded to, is in biophysics, and the fact that keeping muscle cells contracted requires continual energy supplying; but this is a matter of biology, not physics.

• What do you think of requiring energy to decrease the entropy, rather than simply keeping it at a lower value?
– BMS
Commented Feb 18, 2014 at 6:06
• This just avoids the question. Why does energy need to be supplied in order to keep in the same thermodynamic state? One can imagine a simple model wherein the polymers in your rubber band tend to (entropically) shorten, but every time they begin down that path they are pulled taut again by a regulatory mechanism. Useful energy is turned into heat via all the little pushes required to keep deviations from tautness small. Gravity, on the other hand, alters the potentials so as to make spontaneous shortening unlikely. There is a fundamental difference.
– user10851
Commented Feb 18, 2014 at 8:05
• @ChrisWhite: True, although the OP seemed more interested in whether the continual energy expenditure was something fundamental to physics or had to do with biology, and it's biology, so I didn't really touch on the physics much. If you post the gravity potential explanation, I'm sure people'd find it useful too. Commented Feb 18, 2014 at 14:20

Put the object on a table. Nothing happens, table or object. Your meat is metabolizing about 2000 Calories/day basal metsbolism, 8.4 million joules/day. "There is only about 0.1 mole of ATP in the body, but daily energy needs require 100 to 150 moles, or about 50 to 75 kg. The average human adult will use their body weight in ATP each day – so ATP must be recycled as it is used."

http://gasexchange.com/notes/metabolism/

The physics is wholly independent of the biology.

• I don't know that this addresses the OP's question. Eliza is looking for a connection to an entropy-way of looking at things.
– BMS
Commented Feb 18, 2014 at 6:03