Question

State the second law of thermodynamics. How is a heat engine different from a refrigerator?

Answer 1

Hint: Both first law and the second law of thermodynamics are related to heat transfer or energy transfer between two systems. The first law of thermodynamics gives an idea about the quantity of energy transferred between two systems whereas the second law of thermodynamics gives an idea about the quality of energy transferred between two systems. The second law of thermodynamics also digs deep into the direction of energy transfer between two systems.

Complete step-by-step solution:
The second law of thermodynamics talks about the quality of energy transfer as well as the direction of energy transfer between two systems. This law actually puts restrictions on the direction of energy transfer as well as the efficiency of heat engines.
The second law of thermodynamics states that when a spontaneous process occurs, the entropy of the universe increases. In other words, the entropy of an isolated system never decreases over time. This suggests that the change in entropy of the universe can never be negative. Mathematically, the law can be expressed as
$\Delta {{S}_{universe}}>0$
where
$\Delta {{S}_{universe}}$ is the change in entropy of the universe
Let us understand the law using the example of an isolated system. Firstly, let us consider an isolated system that is unaffected by external thermodynamic quantities like temperature or heat. The entropy of this isolated system refers to the measure of energy inside the system. This isolated system transfers heat with the surroundings, to create a change in entropy of the system, provided the mass of the system is constant. The law states that this change in entropy will always be positive. Further, the movement of molecules in this isolated system can also create a change in entropy. Again, the second law of thermodynamics states that this change in entropy is positive.
The second law of thermodynamics has been stated in many ways by famous personalities of all time. Let us understand two such varied versions of the Second law of thermodynamics to understand the working of a heat engine as well as a refrigerator.
Kelvin-Planck statement of the Second law of thermodynamics states that it is impossible to create a heat engine which absorbs heat from a hot reservoir and converts all this heat to mechanical energy or work.
A heat engine absorbs heat from a hot reservoir, converts some of this heat to mechanical energy or work, and releases the remaining heat to a cold reservoir. If ${{Q}_{H}}$ is the heat absorbed by the heat engine from a hot reservoir and ${{Q}_{C}}$ is the remaining heat released to a cold reservoir after converting a part of ${{Q}_{H}}$, then, the efficiency of the heat engine is given by
 $\varepsilon =\dfrac{{{Q}_{H}}-{{Q}_{C}}}{{{Q}_{H}}}=1-\dfrac{{{Q}_{C}}}{{{Q}_{H}}}$
From this expression, it is clear that the Kelvin-Planck statement is true because a hundred percent efficient heat engine is impossible to create.
Clausius’s statement of the Second law of thermodynamics states that it is impossible to create a refrigerator that can transfer all the heat absorbed from a cold reservoir to a hot reservoir without the input of energy of work.
A refrigerator absorbs heat from a cold reservoir (making it even cooler), converts a part of it to mechanical energy or work, and releases the remaining heat to the surrounding hot reservoir. If ${{Q}_{C}}$ is the heat absorbed by the refrigerator from a cold reservoir and if $W$is the mechanical energy or work done by the refrigerator, the coefficient of performance $(COP)$ of the refrigerator is given by
$COP=\dfrac{{{Q}_{C}}}{W}$

Note: Students can relate Kelvin-Planck statement of Second law of thermodynamics and the working of a heat engine to understand the restriction put forth by the law on the efficiency of heat engines. They can also relate Clausius’s statement of the Second law of thermodynamics and the working of a refrigerator to understand the restriction put forth by the law on the direction of energy transfer.