Chapter 5: Thermodynamics (C1313417)

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Thermodynamics is the science of energy, and its relationship with macroscopic properties. Macroscopic is large-scale analysis, that doesn’t require atomic or molecular concept. Because of the probabilistic nature of thermodynamics, it requires a large sample, and therefore, only predicts a large number of atoms or molecules, which can only be found in a macroscopic body.

“God can of course be experienced,” Emily concurred, “but why does it work sometimes, and sometimes not. That seems probabilistic to me?”

“Three reasons: (1) we can’t see the result, because of our perspective,” Mandy replied, “if it is not answered, it is because (2) it inhibits another person’s free will, and God isn’t willing to do that; or (3) it isn’t the best outcome in the bigger picture.”

“He ALWAYS answers prayer,” Blaire continued, “only, that it’s with what you need, rather than just want.”

Continuing on from the discussion on the 1st law of thermodynamics in a closed system $\Delta E=W+q$, in contrast with physics (which was more concerned with work than heat), chemistry is more concerned with heat. Heat transfer is from hot to cold, and can be divided into:

• Conduction, which is the transfer of heat energy by particle collision, such that the energetic molecules lose energy to the less energetic molecules. For example, metals are thermally conductive, as the free electron see permits particle collision to occur. Conductance requires physical contact between the bodies. Thermal conduction (through a hypothetical metal bar) is analogous to electrical conduction, and also fluid flow (through a pipe). Analogous to how volumetric flow rate (in fluids) is related to pressure difference between two points ($\Delta P=QR$), heat flow rate is related to temperature difference between two points. Heat flow rate [and hence also volumetric flow rate] is analogous to current in electricity. Pressure difference [and hence temperature difference] is analogous to voltage (electrical potential difference) in electricity. Also, analogous to Poiseuille’s law ($\Delta P=\dfrac{8\mu LQ}{\pi r^4}$) which states that volumetric flow rate is related to (some derivative of) area ($\pi r^4$), and inversely related to length, heat flow rate is related to cross-sectional area (of the bar), and inversely related to length (of the bar).Note that this relationship is also analogous to electrical resistance ($R=\dfrac{\rho l}{A}$), because given $V=IR$, current is inversely related with resistance, meaning current is directly related with area, and inversely related to length, quod erat demonstrandum (for both heat and fluid flow). Analogous to how ideal fluid flow rate is constant throughout the entire fluid, heat flow rate is constant throughout the bar
• Convection, which is the transfer of matter (large group of particles), therefore transferring with it the related energy of the particles. For example, convection current causes hot air to rise and cold air to fall, and causes hot water to rise and cold water to fall. Blood also utilizes the same mechanism, carrying excess heat (by internal organs) to the skin
• Radiation, which is emission of heat (from matter) through electromagnetic radiation. All matter emits radiation. For example, skin radiates heat (to surrounding cooler objects) to rid the skin of heat. The Stefan-Boltzmann law states that the radiation emitted is proportional to the area, and proportional to temperature (in Kelvins) (to the 4th power). Note that the skin is both receiving (from hotter objects) as well as emitting heat (to cooler objects)

With work, in contrast with physics (which per $W=F\bullet d$, is concerned with work over a distance), chemistry is more concerned with work on an object at rest, known as pressure-volume work (aka pV work), where the volume [of gas] expands against the opposing pressure [of the atmosphere]. Volume expansion causes a piston to move, thereby causing work [as work is related to distance]. Where pressure is constant, (pV) work done is $W=P.\Delta V$. Note therefore, if there is no volume change ($\Delta V=0$), no pV work is done.

2nd law of thermodynamics is the law of entropy, that thermal energy cannot be completely converted into work in a cyclical process. In other words, energy becomes increasingly unavailable to do further work [ever again]. It explains why perpetual motion machines, which try to continue indefinitely without an external energy source, are impossible.

State functions are properties of a thermodynamic system, which depend on the current state, and specifically do not depend on the process of how the state was acquired (known as pathway independent). State functions include:

• Internal energy ($U$), which is the combination of the energies of a system’s (microscopic) particles. These can be divided into three kinetic energies (aka thermal energies), and three potential energies. The thermal energies include translational, rotational and vibrational energy. Translational and rotational is per definition of translational and rotational inertia, and vibrational relates to oscillation per discussed too. The potential energies include rest mass energy, electronic energy, and chemical energy. Rest mass energy is the mass-energy equivalent ($E=mc^2$) energy as  discussed . Electronic energy relates to the electrostatic energy between the atomic nuclei and electrons. Chemical energy relates to the energy stored in intermolecular chemical bonds. Only the kinetic energy portion [of internal energy] gives rise to temperature of the system, meaning only an increase in kinetic energy causes an increase in temperature (of a substance)
• Temperature ($T$), which measures the average kinetic energy of particles. Specifically, kinetic energy due to (rapid) translation in fluids, and vibration about a fixed point in solids. Systems can have the same internal energy, but be at different temperatures, because internal energy depends not only on temperature, but also number of particles. Specifically, systems at higher temperature (with the same internal energy) have less particles. Temperature is measured in Kelvins, or degree Celsius (aka centigrade). Kelvins is related to degree Celsius by the equation $K=C+273$. The SI unit of temperature is Kelvin, and is an absolute scale, meaning 0K is the very minimal temperature possible; where particles are as close as possible to complete rest, having only minimal motion. [This is not the same with $0^{\circ}C$.] 3rd law of thermodynamics is that absolute zero can [be experimentally approached, but] never be achieved
• Enthalpy ($H$), which is $H=U+pV$, where $H$ is enthalpy, $U$ is internal energy, $p$ is pressure, and $V$ is volume. Enthalpy measurement is expressed as a reference against the standard state, of $25^{\circ}$ and 1 bar [approx. 1 atm] ideal gas, or 1M concentration of solute [in solution], which is usually indicated by a degree sign ($^{\circ}$) [which is indifferent from STP, which was $0^{\circ}$ and 1 atm], meaning these enthalpies are 0. Enthalpies of compounds (non-elements) can be calculated by the enthalpy changes from 1 mol of its elements in standard state, known as the (Standard) enthalpy of formation, represented by $\Delta H_{f}^{\circ}$. Where there is no change in pressure or volume, $H=U$. Since internal energy is often thought of as heat, enthalpy is thus also often thought of as heat too, $Q=\Delta H$. In fact, enthalpy change is the heat of reaction, $\Delta H=H_{t}-H_{0}$, where $\Delta H$ is enthalpy change, $H_{t}$ is the enthalpy [of formation] of the products, and $H_{0}$ is enthalpy [of formation] of the reactants. This suggests that the reactants break down into its elements, and then forms its products [which does not occur], but is correct because of Hess’ law [of heat summation], which states that enthalpy change is the same whether the reaction is made in one or several steps, based on the fact that enthalpy is a state function, which is pathway independent. When $\Delta H$ is positive, it is an endothermic reaction, and heat is absorbed; and when $\Delta H$ is negative, it is an exothermic reaction, and heat is released. This can be memorized with the mnemonic that “exo” means that heat “exits”, so you have to subtract the heat, and hence it is “negative”; and “endo” means that heat “enters”, so you have to add the heat, and hence it is “positive”. Energy diagrams illustrate the change in energy of the reactants to the products, the hill representing the transition state, which is the [non-isolatable] chemicals found at the top of the hill. In contrast, an intermediate state is isolatable, occurring between two hills. The height of the hill [from the reactants] represents activation energy (energy required to break bonds of reactants) for the forward reaction. The height of the hill [from the products] represents activation energy for the reverse reaction. The difference in energy between the reactants and products, is the enthalpy ($\Delta H$). Catalysts do not alter enthalpy; rather, they alter activation energy required, thereby, increasing the rate of both forward and backward reaction

[img]catalyst-effect-on-activation-energy.png[/img]

• Entropy ($S$), which is a measure of the system’s disorder, which if applied to the probability of molecules diffusing from one area to another adjoined area, amounts to randomness. It is designated as 0, of a pure substance at 0K. 2nd law of thermodynamics can be restated as, entropy never decreases. This can be reconciled with the original definition that this law states that energy becomes increasing unavailable to do work [ever again], because entropy of a system does not just decrease. Rather, it requires the application of work, even when flowing [naturally] from a hot to colder body. Therefore, some energy is required to do this work, and is hence unable to be recycled

Entropy can therefore be written as $\Delta S_{universe}=\Delta S_{system} + \Delta S_{surroundings} + \Delta S_{universe} \ge 0$, and , where $\Delta S$ is the change in entropy. Entropy can also be defined as $\Delta S=\dfrac{Q}{T}$, where $Q$ is the reversible heat transfer into that system, and $T$ is the temperature of the closed system (in Kelvins). A reversible [or quasistatic] process is a hypothetical process that occurs by infinitely small changes, infinitely slowly, thereby not requiring energy, and therefore not increase entropy [and therefore conserving entropy]

“’Dad, since entropy can never decrease, I can never clean up my room,’ Jamie’s daughter says,” Mandy said, “What’s wrong with this statement?”

“Thermodynamics is a macroscopic study, and cannot be applied microscopically,” Jamie replied, “You need to consider not only the system, but also its surroundings.”

• Gibbs [free] energy ($G$), originally called available energy, which is the maximum amount of energy from a reaction, free to do non-PV work. Because the 2nd law of thermodynamics states that energy becomes increasingly unavailable to do work [ever again], Gibbs free energy advises of the maximum amount of energy that can. It is expressed as $\Delta G=H-T\Delta S$, where $H$ is enthalpy, $T$ is temperature, and $\Delta S$ is [change in] entropy [in the system]. If $\Delta G$ is negative, the reaction is spontaneous; if $\Delta G$ is positive, the reaction is non-spontaneous. Note that spontaneity doesn’t indicate the speed of reaction; for example, diamond spontaneously decays into graphite, but this decay is extremely slow and takes millions of years

“Oh my goodness,” Mandy commented, “this would mean that De Beers could be done for misleading and deceptive conduct, with their whole ‘a diamond is forever’ copy writing!”

This indicates that an exothermic reaction ($\Delta H<0$) that increases entropy ($S$) is always going to be spontaneous ($\Delta G<0$), and an endothermic reaction ($\Delta H>0$) that decreases entropy ($S$) is always going to be non-spontaneous ($\Delta G>0$). There is thus only doubt, is when enthalpy ($\Delta H$) and entropy ($S$) have the same sign. Here, we note that high temperature favors spontaneity, and low temperature favors non-spontaneity.

• Pressure ($p$)
• Volume ($V$)

 Learning activity What is thermodynamics? What is thermochemistry?

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