4. Processes where entropy decreases spontaneously. There are many processes in which living matter becomes more organized (e.g., an egg evolving into a bird). This observation has led certain philosophers and popular science writers to (erroneously) claim that life does not obey the 2nd law. Here we analyze a simple process, in which a system becomes more organized spontaneously, from the 2nd law perspective. Consider a jar of honey inside your fridge, which we will consider to be a constant temperature and pressure environment. After an appropriate center of crystallization is placed inside the jar (bread crumbs work well) it eventually becomes crystallized. (Honey is an example of a supercooled liquid, which is stuck in the wrong phase below its crystallization point. Adding a crystallization center helps getting it unstuck triggering spontaneous crystallization process. We will learn more about supercooled liquids soon). A. Did the entropy of honey increase or decrease as a result of this process? B. Does the result of part A contradict the 2nd law? Explain your answer mathematically by writing down the 2nd law in a form of an inequality and verifying whether or not this inequality is satisfied. (Hint: does the honey exchange heat with the surroundings? Which way does the heat flow if it does?) C. Did the Gibbs free energy G of the honey increase, decrease, or remain constant as a result of this process? Explain your answer mathematically again by writing the definition of G and using your results from parts A and B. D. Suppose that immediately after crystallization is initiated, the honey is transferred into a thermally insulated container. This is done quickly enough that the temperature of the honey does not change during the transfer. Will the honey continue to crystallize after that? E. Will the entropy of honey increase, decrease or stay the same as a result of the process it undergoes after being thermally isolated? F. Do the conclusions you have arrived at in Parts D and E contradict one another? Explain your answer. 4. Processes where entropy decreases spontaneously. There are many processes in which living matter becomes more organized (e.g., an egg evolving into a bird). This observation has led certain philosophers and popular science writers to (erroneously) claim that life does not obey the 2nd law. Here we analyze a simple process, in which a system becomes more organized spontaneously, from the 2nd law perspective. Consider a jar of honey inside your fridge, which we will consider to be a constant temperature and pressure environment. After an appropriate center of crystallization is placed inside the jar (bread crumbs work well) it eventually becomes crystallized. (Honey is an example of a supercooled liquid, which is stuck in the wrong phase below its crystallization point. Adding a crystallization center helps getting it unstuck triggering spontaneous crystallization process. We will learn more about supercooled liquids soon). A. Did the entropy of honey increase or decrease as a result of this process? B. Does the result of part A contradict the 2nd law? Explain your answer mathematically by writing down the 2nd law in a form of an inequality and verifying whether or not this inequality is satisfied. (Hint: does the honey exchange heat with the surroundings? Which way does the heat flow if it does?) C. Did the Gibbs free energy G of the honey increase, decrease, or remain constant as a result of this process? Explain your answer mathematically again by writing the definition of G and using your results from parts A and B. D. Suppose that immediately after crystallization is initiated, the honey is transferred into a thermally insulated container. This is done quickly enough that the temperature of the honey does not change during the transfer. Will the honey continue to crystallize after that? E. Will the entropy of honey increase, decrease or stay the same as a result of the process it undergoes after being thermally isolated? F. Do the conclusions you have arrived at in Parts D and E contradict one another? Explain your