I have read the Karlsruhe physics online courses and the authors are adamant that entropy is just what people call heat in daily life, not to be confused with heat as transfer of energy.
Do you think that this statement is true?
Disclaimer: I don't advocate this theory. I want to ask why it is wrong or correct
No, it's not true. Entropy and heat are very closely related, but it's confusing and wrong to say they're the same. I suppose you could say, very informally and with some hand-waving about units, that what people informally call heat is one form of entropy. However, there are also other forms of entropy that are not heat.
As an example, consider what happens when you stretch an elastic band out for a while and then let it contract again. When the elastic relaxes, it cools down. Why? Because the relaxed rubber has a greater entropy than in the stretched state (follow the link for more details of why), and this means that entropy in the form of heat can be converted into entropy in the form of molecular configurations, allowing the amount of heat to decrease while the total entropy stays more or less the same.
It should be stressed though, that this is all really informal language and not quite correct. (In particular, there is not really such a thing as "the amount of heat".) If you want to learn the subject properly there isn't really any substitute for learning the proper language that physicists use to describe thermodynamics, and it's important to keep in mind that this way of thinking about it isn't quite correct.
In thermodynamics, heat is defined as the process of transfer of energy.
So you can't ask, how much heat an object has, only how much energy is going in or out of the system during some time period.
The definition of entropy is dependent on the area of physics you are dealing with, in thermodynamics it is defined as $S = k ln \Omega$.
If this looks too maths based for you, read this page Entropy and you might appreciate how straightforward it is, compared to the complications involved in explaining entropy in words.
Entropy is a measure of the number of states a system, such as those in which container of gas might be found in, over a period of time.
The main difference between energy and entropy is that energy is conserved, but entropy is not conserved and will increase over time.
Entropy, $$\Delta S = \frac QT $$ provides us with a way to state the second law of thermodynamics.
Enthalpy, $$H=U+PV$$ is a quantifier of internal energy such that $P$ and $V$ are the pressure and volume, and $U$ is the internal energy. Enthalpy is an analogue of the first law of thermodynamics $$\Delta U=Q-W$$ applied to the case of constant pressure systems, $$Q=P\Delta V + \Delta U$$ hope this helps.
You may be talking about enthalpy. Enthalpy in the heat content of a body at constant pressure.
Entropy is just the degree of randomness.
Let me first link to an article of the authors of the Karlsruher Physikkurs (KPK), where they justify their belief that entropy corresponds better to what people intuitively think of as 'heat'.
Herrmann, Pohlig, Which Physical Quantity Deserves the Name “Quantity of Heat”?
Concerning the accepted answer and the rubber band example: it seems to me like that's not a good rebuttal of the KPK's claim. From the KPK's perspective, it might be explained like this (please correct me if I get the physics wrong or if I got the KPK intrepetation wrong): The process is reversible to a good approximation; hence, entropy is conserved and only moved in and out of the band. When the band is stretched between our lips, entropy moves out into our lips, which we perceive by our lips getting warmer; when it is relaxed, entropy from our lips goes back into the band, hence we feel the cooling. This fits well with a layperson's idea (and this is one of the KPK's claims) that heat might be something that's located somewhere in space and can be shifted around, hence is intuitively thought of as an extensive quantity. The same can't be said of the modern definition of heat, which is a process quantity.
To me, a more 'counterintuitive' example to challenge the KPK's claim is the irreversible process of placing a hot and cold body in thermal contact and letting them get to thermal equilibrium. Here, entropy is moved and generated, but I don't think a layperson would imagine that 'heat' (in whatever everyday sense) is being generated in this process.
