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Applicability of First and Second Laws of Thermodynamics
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First Law in its simplest form - Energy cannot be created or destroyed, but can change form, and location. For instance, burning wood changes the internal energy in the wood into heat and light energy.

Second Law - The Second Law is the most understandable and useful in real world applications, and makes heating, air conditioning, and refrigeration possible. Energy must flow from a higher state to a lower state. That is, heat must always flow from the warmer object to a cooler object and not from the cooler object to the warmer object.

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The Second Law holds in our everyday visible world, but on the subatomic level the law is constantly violated, but statistically the law holds true.

Heat Engine

Heat Engine is a system that partly converts heat into work, i.e. a system that coverts thermal energy into Mechanical Energy.. Work and Heat are two conjugate variables and two different ways of influencing the internal energy of the thermodynamical system.

1st law of thermodynamics says that change in the internal energy ΔU ( in closed system) is equal to the amount of heat Q supplied, minus the amount of work done by the system on its surroundings. This is done by a working substance from higher temperature zone ( source ) to lower temperature zone ( sink ). This is done by converting some thermal energy into work. The larger the difference in temperature between the source and sink, the higher is the potential thermal efficiency of the cycle.

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Burning fuel in the engine (increasing it’s thermal energy due to heat transfer) will cause the engine to move (to perform work). There is no way of changing all delivered heat to work. That is why, a car engine gets hot, dissipating a lot of it’s thermal energy. It's another way of stating the second law of thermodynamics, that no cyclic process can completely convert heat into work.

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How does heat flow from a colder region to a warmer region?

This would of course violate the second law of thermodynamics

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However, if you do some work on the system, which is what a refrigerator does, then it does not violate the second law.

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An input of mechanical work would be required to do this (compressor in a refrigerator). A refrigerator is thus essentially a heat engine operating in a reverse cycle.

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