Spontaneous & Nonspontaneous Processes By Alec Gautier

Nature’s Heat Tax Heat Tax: the amount of energy lost during an energy transaction In every energy transaction, a portion of the energy will always be lost to the environment. *However, the energy is not literally lost as that defies the first law of thermodynamics. Rather the “lost” energy is dissipated into the environment and absorbed by its surroundings. Example: When driving a car, much of energy that goes toward powering it is absorbed by the engine during the combustion of gasoline. Only about 20% of the energy it takes to move a car forward goes toward actual locomotion. *In summary, the concept of perpetual motion is impossible, humans can only hope to create more efficient machines

Practice question 1 Which of the following methods of heating one’s home would be most efficient? WHich method is least efficient? A. Natural Gas B. Electrical heating C. SOlar energy D. Hydropower Answer: Natural gas is most efficient and Electrical heating is least efficient.

Spontaneous and nonspontaneous processes Spontaneous process: A process that occurs without outside intervention. Nonspontaneous process: A process that requires energy in order to occur. * Do not confuse the spontaneity of a reaction with the speed at which it occurs, the two are unrelated. The rate of a reaction is related to kinetics. Nonspontaneous reactions cannot be made spontaneous through the use of a catalyst. Catalysts only affect the reaction rate.

dialogue 1 Class: So, accepting the notion that nonspontaneous reactions are impossible through the use of a catalyst, can nonspontaneous reactions occur? Me: Of course! In order for a nonspontaneous reaction to occur, the process must either have outside energy applied to it or the reaction must be coupled with a spontaneous reaction.

Practice question 2 Which of the following reactions is nonspontaneous? A. Iron Rusting B. Diamond becoming graphite C. Ice melting D. a car moving Answer: D *Although diamond becomes graphite at a remarkably slow rate, the process still takes place without intervention.

Dialogue 2 CLass: Wait a minute, how can something like ice melting be considered spontaneous, as the reaction is endothermic and the product has more energy than the reactant? If there was no intervention, where does the energy required to melt the ice come from? Me: Well, that is due to the universe’s tendency toward higher entropy. Class: what does that mean?

An introduction to entropy ENtropy: (in general) A measure of the randomness of a system Entropy: (Specifically) A thermodynamic function that increases with the number of energetically equivalent ways to achieve a particular state. Example: When you dissolve salt in water, the entropy of the system increases because the salt particles lose their shape and the arrangement of the molecules / ions becomes more disorderly. There's also a mathematical way to calculate entropy using this formula… ENtropy (S) = boltzmann Constant (K) ln (W) *Boltzmann Constant = 1.38x10(to the -23rd) j/k

What is (W)? In order to understand (W), one must first understand macro and microstates. Macrostate: The overall state of a system. Example: We measure an ideal gas with the formula PV=nRT. While this formula gives us the measurements of a gas, it only provides us with the general state of the system, or macrostate. However, the measurements of individual particles during various moments cannot be determined by calculating the macrostate of a system, as at one point a particle could have lots of energy whereas at other points it could have much less energy. Microstate: The exact internal distribution of energy and location of individual particles.

So what is (W) then? Simply put (W) = the possible number of microstates that can occur within a macrostate. Example: Given the two systems A and B in the picture below, both systems have the same total energy of 4 joules, however system A has 1 microstate and system B has two.

Practice question 3 Given the definition of a microstate and the picture from before, which system has the greater (W) value? Which system has the greater entropy? Answer: System B, because it has 2 microstates. (W) = number of microstates that can occur within a macrostate. Answer: System B, because it has 2 microstates, or 2 different possible arrangements of the particles. *Since entropy is greater with in systems more energetically equivalent ways arrange its particles, we can generalize that the system with the greatest entropy also has the greatest dispersal of energy amongst its particles.

Second Law of Thermodynamics Second Law of Thermodynamics: For any spontaneous process, the entropy of the universe increases. Second Law of Thermodynamics: (change in Entropy of the universe > 0) *A process is considered spontaneous if it increases the entropy of the universe. *All processes that are spontaneous increase in entropy! *systems alway trends toward higher entropy! To find change in entropy, you just do final entropy - initial entropy. With the above formula, if your change in entropy value is positive, the reaction is spontaneous.

Entropy change associated with change in state Since we know that entropy increases when there are more energetically equivalent ways to arrange particles in a system, it makes sense that s(solid) < s(liquid) < s(gas). Energy can also distributed by particles in more ways than just movement (translation). Energy can be distributed throughout a system by particles vibrating and rotating.

Final question Emily...