Increase in entropy without change in temperature

[zorro]

Can heat supplied to a body increase its entropy without even changing its temperature? I recall that increase in randomness is accompanied by a change in temperature.

 

[Bill_K]

Yes, for example if you boil water the water vapor will have greater entropy than the liquid water, while the temperature remains constant.

 

[Andy Resnick]

Can heat supplied to a body increase its entropy without even changing its temperature?

Yes- a general expression for the heat flow Q during a process is:

$$Q = \Lambda_{V}(V,T)\dot{V} + K_{V}(V,T)\dot{T}$$

Where K is the specific heat at constant volume and $\Lambda$ is the latent heat at constant volume. Thus, for example, heat can be supplied to expand a gas, increasing the entropy- the volume changes and the temperature remains constant.

Also, phase changes (often with reference to the latent heat of melting/boiling/freezing/...) can be accompanied by a flow of heat without a change in temperature. Folding/denaturing of proteins and macromolecules is also a process involving isothermal changes to energy and entropy.

Using the term 'randomness' to describe entropy should be resisted.

 

[zorro]

Using the term 'randomness' to describe entropy should be resisted.

I am eager to know the reason for it.

 

[jschmidt]

I am eager to know the reason for it.

I think because, while randomness is one aspect of entropy (I think?) it's not the only aspect. I think 'density' of energy is also an aspect of it. As energy becomes more diffuse, I think, entropy is said to increase?

I have to admit that I find, currently, Entropy to be one of the more confusing topics in physics. I'm still trying to get my head around it, but I think density of energy is part of entropy.

Also, randomness, is usually more of a mathematical concept of how easy/hard it is to predict something. Is Iron more or less random than Uranium or Hydrogen? I'm not sure about this, but I *think*, that since it's nearly impossible to get net energy out of Iron, because it is at the most stable point on the curve of binding energy, it is at a higher entropic state than Hydrogen (which you can cause to undergo thermonuclear fusion to release energy), Or Uranium, which can undergo nuclear fission to release energy.

My current 'best understanding' of Entropy is that the lower the entropy of a system, the easier it is to extract useful work or other energy-driven changes (chemical reactions, emmission of radiation, etc) from the system. The higher the entropy, the less you can cause change using that energy.

 

[Andy Resnick]

I am eager to know the reason for it.

Because "randomness" is not always precisely defined. In order to use the term "randomness" in the context of entropy, you must be precise about what 'randomness' means- and that may be trivial or not, depending on how you use the term regarding information content, ensemble averaging, ergodic or nonergodic systems, etc.

Here's an example- flip a coin 100 times, each time writing down either a '0' or '1', depending on the outcome of the toss. Compared to a string of 100 '1's, Does that string of 100 binary digits have higher or lower entropy? Does it have higher or lower information content?