There is no accepted or established "fourth law of thermodynamics". There are, however, numerous authors who have postulated versions of fourth laws to explain certain aberrant phenomena. The following link gives over fifteen different versions of postulated "fourth" laws of thermodynamics: http://www.humanthermodynamics.com/4th-Law-Variations.html
"Unavailable for doing work" is related to the Second Law of Thermodynamics.
Thermodynamics is both a law and a theory. It has a set of well-established laws, such as the first and second laws of thermodynamics, which describe the behavior of energy in systems. Additionally, the principles and concepts underlying thermodynamics are formulated into a theory to explain and predict the behavior of physical systems.
Second Law of Thermodynamics
The Second Law of Thermodynamics.
the internal energy (thermal energy)
Not exactly. The first law of thermodynamics, i.e. the law of conservation of energy, also accounts for heat as one of the many forms that energy can take. There is no one law called "the law of thermodynamics", but there are several "Laws of Thermodynamics" (note the plural form "LAWS").
Thermodynamic cycle is based on 2nd law of thermodynamics.
Magic
The 1st Law of thermodynamics is a restatement of the law of conservation of energy.
The first law of thermodynamics is also known as the Law of Energy Conservation.
"Unavailable for doing work" is related to the Second Law of Thermodynamics.
Entropy is closely related to the 2nd law of thermodynamics, not the 1st law. The 1st law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. Entropy, on the other hand, is a measure of the disorder or randomness of a system, which increases over time according to the 2nd law of thermodynamics.
That law is known as the Law of Conservation of Energy. It is also known as the First Law of Thermodynamics.
The fact that usable energy is always lost in an energy transfer is due to the second law of thermodynamics. This law states that entropy, or disorder, tends to increase over time in a closed system, leading to the loss of usable energy in the form of heat.
Thermodynamics is both a law and a theory. It has a set of well-established laws, such as the first and second laws of thermodynamics, which describe the behavior of energy in systems. Additionally, the principles and concepts underlying thermodynamics are formulated into a theory to explain and predict the behavior of physical systems.
The first law of thermodynamics states that energy cannot be created or destroyed in an isolated system; it can only change forms. This law is also known as the Law of Conservation of Energy.
There is no commonly accepted law by that name, as far as I know. Two important laws about energy are the First Law of Thermodynamics and the Second Law of Thermodynamics.