There are four laws of thermodynamics.
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.
The 1st Law of thermodynamics is a restatement of the law of conservation of energy.
Magic
The first law of thermodynamics is also known as the Law of Energy Conservation.
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.
"Unavailable for doing work" is related to the Second 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 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.
That's related to the First Law of Thermodynamics - the Law of Conservation of Energy.
second law