Thermodynamics

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Thermodynamic: Thermodynamics simply describes the movement of heat. It deals with heat related motion or other effects. Thermodynamics is derived from thermo, meaning heat, and dynamics, (literally “power”), and is used to describe the movement or change of a process due to heat flow. All below material is relevant only for thermal related energy or work.

NOTE: I've included Thermodynamics as part of Chemistry as that is where it's grouped under in most courses, although it could as well be part of Physics, as it invloves Energy, work, etc.

Any object has observable properties as Temperature, Pressure and Volume. These are macroscopic properties observed at object level, but all these objects are made of microscopic components called atoms, which combine to form molecules. Each of these molecules has a distinct state such as position and velocity, which ultimately decides the microstate of each molecule. Microstate of all these molecules combined define the macrostate of the system/object that we observe.

Entropy: It is the measure of how disorganized and random a system is.

Entropy is defined as all possible microstates that the system can occupy. If each state "i" has a probability pi of being occupied, then entrpoy (S) is =>

S = -kb Σ pi log (pi) => Here kb=boltzmann constant = 1.38x10^-23 J/K. So, unit of S is also J/K. Kb provides conversion from Temp to Energy and represents the energy of a particle per unit temperature. So, a particle at 0K has 0 energy but one at 100K has 1.38*10^-21J (multiplying Kb by 100)

If a system has Ω number of possible microstates, and each microstate has equal probability of happening, then S = -kb * Ω * 1/ Ω * log (1/ Ω) => S=  kb*log( Ω). This is true for an isolated system in equilibrium. In thermodynamics, such a system is one in which the volume, number of molecules, and internal energy are fixed.

In other words, entropy measures the disorder or uncertainty about a system, i.e billions of different possible microstates that the system can have, can give rise to uncertainty as to what state the system is in now. If there are 50 molecules of water, and each molecule of water can be in 10 different states, then total number of possible states is 10^50 (since each molecule can be in any of 10 states, and there are 50 molecules, so simple probability says it is 10 multiplied 50 times). So, entropy is kb*log( Ω) = kb*log(10^50).

NOTE that entropy is a measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Every system has internal thermal energy in it, that keeps atoms vibrating. As we cool things, things change from gas to liquid (less vibration), then to solid (even less vibration), then start getting into more perfect lattice. If we go to very low temperature close to 0K, we will get lattice structure where there is no vibration, and each atom of lattice is exactly the same way as any other atom. There is no variation or disorder in this lattice structure. It behaves like a perfect crystal, one in which the internal lattice structure extends uninterrupted in all directions. Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.  Possible number of micro states is just 1 which is the ground state (since each atom has only 1 state (no vibration), so irrespective of number of atoms, there can be only one state for system, as all atoms will have that 1 state). In this case entropy = kb * (log 1) = 0. 

So, at absolute zero temperature (0 Kelvin or -273.15C), entropy of a system should ideally be 0 (i.e only single ground state possible for all atoms). However, in reality perfect crystal structure is not achieved even at 0K. There are other micro states besides the ground state. In other words, the system is at lowest internal energy state (least vibration), but not 0. There is still vibrational motion in particles, which cannot be removed. Perfect crystals never occur in practice; imperfections, and even entire amorphous material inclusions, can and do get "frozen in" at low temperatures, so transitions to more stable states do not occur (even though there may be multiple micro states, but we may just see 1 micro state). Correct form of 3rd law of thermodynamics (mentioned below) is that entropy approaches 0 as temperature goes to 0. So, Entropy at 0K is some finite residual value, but for convenience, we take entropy at 0K to be zero, for reference. 

Standard Entropy (S⁰) => It's defined as the entropy of 1 mole of a substance at std conditions - 1 atm pressure and 25C temp.

S⁰ of Solid Carbon (graphite) = 5.7J/mol-K. For H₂O (liquid), it's 69.9 J/mol-K, while for CH₄ (gas), it's 186.6 J/mol-K. As can be seen, Entropy increases from solid -> liquid -> gas as there's an increase in freedom of movement, resulting in more microstates. In general, entropy is higher for a compound with higher molar mass, since that implies more atoms in the compound and hencemore microstates possible.

We can find Entropy of any reaction, by finding Entropy of reactants and products. S⁰ of any Reaction = Entropy of Products - Entropy of Reactants

Ex: Find Entropy of reaction for 1 mole of CaCO₃ (s) -> CaO (s) + CO₂ (g). Here ΔS⁰ of Reaction =  S⁰(CaO) +  S⁰(CO₂) - S⁰(CaCO₃) = 1 mole*39.8 J/mol-K + 1 mole*213.6 J/mol-K  - 1 mole*92.9 J/mol-K = 160.5 J/K for 1 mole of reactant.

Three Laws of Thermodynamics:

Just like we have Newton's laws for motion, we have 3 separate laws for thermodynamics (as no other laws explain thermal observations. Newton's laws are limited to mechanics). There is also a “Zeroth”L aw that states, in a rather complicated way, that no heat will flow between two objects that are at the same temperature. This seems so obvious that this law is generally ignored, in common practice.

First Law- 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.

In other words, it states that the change in internal energy of a system (sum of KE + PE) = q + W, where q=heat energy transferred to (+ve q) or taken out (-ve q) from the system, while W=work done on (+ve W) or by the system (-ve W).

ΔU = q + W (NOTE: it's change in internal energy in this eqn, not internal energy itself. q and W are not changes, but rather absolute values)

Enthalpy: To measure the energy changes that occur in chemical reactions, chemists usually use a related thermodynamic quantity called enthalpy (which in greek means to warm).

Enthalpy of reaction => https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/05%3A_Thermochemistry/5.04%3A_Enthalpy_of_Reaction

Enthalpy is defined as the sum of its internal energy plus the product of its pressure and volume: H = U + PV, where U=internal energy of system, P is pressure and V is volume of the system. 

Change in enthalpy ΔH = ΔU + (ΔP)V + P(ΔV). If a chemical change occurs at constant pressure (i.e., for a given P, ΔP=0), then eqn reduces to ΔH = ΔU + P(ΔV). Work done by the system W = -P(ΔV) (with a -ve sign) as when vol inc (ΔV is +ve), then system does the work, so W has to be -ve and vice versa. So, ΔH = ΔU + P(ΔV) = q_p + W +(-W) =  q_p where q_p is the heat energy at const pressure . So, change in enthalpy is the heat energy gained or lost at const pressure, i.e  ΔH = q_p (If heat is gained, then ΔH is +ve (endothermic reaction), while if heat is lost, then ΔH is -ve (exothermic reaction)).

If system is held at constant volume, then W=0 (as extra pressure with no movement gives 0 work). So, change in internal energy  ΔU = q_v + W => ΔU = q_v where q_v is the heat energy at const volume.

Why define Enthalpy this way? To help understand why we defined enthalpy as U+PV, we need to understand that enthalpy was introduced as a way to measure the heat energy supplied to a reaction, that will get into as internal energy of the reaction. This heat energy supplied to the reaction will increase the internal energy of the reactants/products, but some of the energy will also get wasted in doing work by the system (i.e gaseous molecules fighting against the atmospheric pressure to expand). There's no way to eliminate W from the system, as this work happens automatically. We are mostly interested in heat energy supplied. ΔH =  q_p measures that by saying that at const pressure, whatever is the change in heat energy supplied, we will call it Enthalpy. Note that not all of this heat energy (Enthalpy) goes as internal energy, some of it goes as W (work done on/by the system) depending on pressure and volume change. For a liquid reaction, there's no change in volume and pressure, so we can consider W ~= 0 => change in enthalpy is almost the same as change in internal energy.

Enthalpy is reported in units of KJ/mole, since enthalpy will depend on molar concentration of substance, more the substance more the energy consumed or produced. 

Change in Enthalpy of a reaction is written alongside the reaction. ex: 2Al + Fe₂O₃ -> 2Fe + Al₂O₃  ΔH_rxn = -850 KJ. This indicates that this reaction gives out 850KJ for molar quantities of the reactants shown , i.e 850KJ is released when 2 moles of Al reacts with 1 mole of Fe₂O₃. We also write this as -850 KJ/mol_rxn (meaning 850KJ per mole of reaction, based on moles of reactants shown in the eqn).  We can also write as ΔH = -850 KJ/mole of Fe₂O₃ or ΔH = -425 KJ/mole of Al. We can also write eqn as 2Al + Fe₂O₃ -> 2Fe + Al₂O₃ + 850KJ indicating that heat is generated as product (i.e heat is given out), since it's written on RHS.

ex: 2H₂O₂ (l) -> 2H₂O (l) + O₂ (g) ΔH_rxn = -196 KJ/mol_rxn . What is the q_p of the reaction when 5 g of H₂O₂ is used? 

Soln: q_p = ΔH_rxn =  -196 KJ/mol_rxn * 1 mol_rxn / 2 moles H₂O₂  * 1 mole H₂O₂ / 34g * 5g = -196/2 *5/34 KJ = -14.4 KJ (we use a technique called matching dimensions, where we keep cancelling moles with moles, g with g, etc) 

ex: AgNO₃ (aq) + NaCl (aq) -> AgCl (s) + NaNO₃ (aq). 25mL of 0.1M AgNO₃ soln reacts with 25mL of 0.1M  NaCl soln in a const presssure calorimeter. Initial temp was 25C, but final temp inc to 26C. What is  ΔH_rxn ?

Molar conc of any soln means that many moles of the chemical per liter of water. So, 0.1M => 0.1Moles of reactants in 1L => 0.0025 moles in 25mL. Total vol of water in reaction = 25+25=50mL. Total heat gained by water = mCΔT = 50g*4.18J/g*1C=209J. This +q gained by water, hence this was given by the reaction, so reaction has q_p =-209J. Since 0.0025 moles of AgNO₃ (aq) and NaCl are present =>  ΔH_rxn =  q_p = -0.2KJ/0.0025moles = -80KJ

Hess's Law: It states that that the total enthalpy change of a chemical reaction is the same, regardless of the number of steps or the pathway taken, as long as the initial and final states are identical.

Enthalpy of Formation of 1 mole of a substance from it's most stable form of constituent elements. It's rep as  ΔH⁰
_f  where "0" refers to that at std conditions (1 atm presuure and 25C), and "f" indicates it's the enthalpy of formation. NOTE: Δ indicates it's the change in enthalpy. Units are KJ/mole. Enthalpy of formation of elements in their most stable state is 0. 

ΔH⁰
_rxn  = ΔH⁰
_f  (products) - ΔH⁰
_f  (reactants)

 ex: C(s, graphite) + O₂ (gas) -> CO₂ (gas) ΔH⁰
_f  = -393 KJ/mole (per mole of reactant and product as shown in reaction). Here, most stable form of carbon is graphite, so it's Enthalpy of formation is 0, same for oxygen gas. 

Writing Enthalpy values of reactions for all possible reactions is not feasible. We have tables for important enthalpy values as shown:

• Enthalpy of combustion (ΔH_comb) The change in enthalpy that occurs during a combustion reaction (virtually any substance that will burn in oxygen)
• Enthalpy of fusion (ΔH_fus) The enthalpy change that accompanies the melting (fusion) of 1 mol of a substance. 
• Enthalpy of vaporization (ΔH_vap) The enthalpy change that accompanies the vaporization of 1 mol of a substance. 
• Enthalpy of solution (ΔH_soln) The change in enthalpy that occurs when a specified amount of solute dissolves in a given quantity of solvent. 

We saw in "Phases of Matter" section, that latent heat of melting of ice->water is 6KJ/mole. That's also the change of enthalpy of this reaction (ΔH_fus), as it takes place under constant pressure (atmospheric pressure). Similarly, latent heat of vaporization of water is 44KJ/mole, which is the enthalpy of vaporization (ΔH_vap) of water.

Second Law- The Second Law is the most understandable and useful in real world applications, and makes heating, air conditioning, and refrigeration possible. It is expressed in many different forms, but they all amount to the same thing. Easiest and most common defn is that 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, unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process, i.e Work can create heat, but not all heat can be converted back to work.

The second law basically is about Entropy and may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of Thermodynamic Equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. 2nd Law of Thermodynamics is also sometimes called as "Law of Entropy", which states that Entropy in Universe is always increasing.

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.

Third Law- As a system approaches Absolute Zero, the entropy of the system approaches a minimum value. Absolute Zero cannot be attained in a real system, it is only a theoretical limit. We saw this above.

Heat Transfer:

Heat can move in three ways: conduction, convection, and radiation.

Conduction is the easiest and most familiar to anyone who has burned themselves on a stove or a hot pot. It is the direct transfer of heat from one object to another, when they are in contact.

Convection is based on the movement of a fluid to transfer heat from one object or area to another. Weather is a convective process; hot air and warm water move from the tropics toward the poles. Here air or water was used as the medium for transfer.

Radiation is heat transferred directly from a source to an object without using a medium like air or water. Heat radiated from the sun will melt snow on the road, even on a cold day. The radiant energy warms the road surface without directly warming the air.

In the real world, the transfer of heat involves a mixture of all three methods, with the possible exception of outer space.

Heat capacity: Defined as the heat needed to raise the temp of an object by 1 degree C. It's the whole amount of object that is present.

Specific heat capacity (C_s): This refers to the heat needed to raise temp of only 1 g of material by 1 degree C. This is the property of a material, and constant for a given material. Unit is J/g-K or J/g-C. C_s varies slightly depending on temp, so we specify C_s at atm temp = 298K (or 25C)

Molar heat capacity: This refers to the heat needed to raise temp of 1 mole of material by 1 degree C. This is the property of a material, and constant for a given material.

Total heat energy needed to raise temp by ΔT of any amount of material is m*C_s*ΔT where C is the specific heat capacity, and m is mass. 

Constant Pressure Calorimeter: Here we keep the pressure const, by having 2 cups, and having the top cup placed inverted on the bottom cup, so that it can slide up or down. That way the vol changes, but pressure inside remains at atm pressure. We have water + small piece of material that we want to measure specific heat of. material is heated to higher temp and put into water at lower temp. Equating heat energies for the two, we find specific heat of the given material. Some heat is lost to surroundings too.

Constant Volume Calorimeter (aka bomb calorimeter): Here we keep the volume const, by having a calorimeter whose walls are rigid. There is water inside it, with a small box in it, in which we put the susbstance in it, which burns by 2 wires coming in to combust the material. The rise in temp of water gives  specific heat of the given material.

Food Calorimeter: The calories present in food is measured by burning that food, and measuring the rise in temp of water, which is heated via this burning. Note that food calories are rep in Calories with capital C, which is 1000 cal (with small c) or 1Kcal. So, don't let this confuse you. See in "food and diet" section for details on unit.

Fermi:

This defn not correct => The Fermi level for electrons of a body is the thermodynamic work required to add one electron to the body. It's the same amount of work to remove one electron from the body. It is a thermodynamic quantity usually denoted by µ or Ef. It's unit is Joules, as it is energy level, not potential level.

 We saw above that each electron in a crystal lattice is in an energy band. However there is a probability distribution that says how many of these electrons will be in which energy level at a given temperature.

The Fermi–Dirac distribution, f ( ϵ ), gives the probability that (at thermodynamic equilibrium) a state having energy ϵ is occupied by an electron:

    f ( ϵ ) = 1 / [e^{(ϵ − μ)/kT} + 1]

Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time. At 0K, since all thermodynamic motion ceases, we would expect that electrons would be frozen, i.e at lowest energy level E0. From above eqn we see that at 0K, all Energy levels below Ef have 100% prob of being occupied, while those above Ef have 0% prob. As is expected at 0K, all these energy states are occupied with 100% certainty, implying only 1 micro state possible (i.e lower N energy states occupied, while upper energy states not occupied. No other combination of energy states possible).

The Fermi level is any energy level having the probability that it is exactly half filled with electrons. Levels of lower energy than the Fermi level tend to be entirely filled with electrons, whereas energy levels higher than the Fermi tend to be empty. Enrgy bands above Ef are called conduction band, while those below Ef are called valence band.

For conducting metals, both conduction and valence band are on each side of Ef right next to it, meaning just little bit of extra energy is needed for these electrons to conduct. Even with no extra energy applied, a lot of thermally active electrons are in conduction band. This causes the electrons to move freely resulting in high conductivity. For insulators, these conduction and valence are further separated out from each other, with Ef in b/w. This means a lot of extra energy is needed for these electrons to conduct. There is a band gap b/w cond and val band, of the order of 10ev. Almost no electrons are in conduction band, resulting in no conductivity. Semiconductors also have these bandgap, are lot smaller bandgap of 1ev. So,  conduction band is very lightly populated with thermally active electrons resulting in low conductivity. Apart from thermal agitation, providing light energy is the other way to move electrons from valence band to conduction band.

NOTE: Fermi level moves around with external voltage applied, so Fermi level is defined with 0 external voltage. Fermi level moves up by "X eV", when "X Volts" applied to the material. So, alternatively, when we say that a conductor is at "X Volts", all electrons have gained an additional "X eV" of energy, so all of the energy band has shifted up by "X eV", so Fermi level has also moved up by "X eV".  So, Fermi level can be known by just dividing voltage of material by "e", if we assign fermi level of 0, for electrical ground (i.e 0 external voltage).  

Work function (W)

As we move higher up in energy band (in conduction band), electrons become more free to move around, but still within the solid material. If we go much higher than conduction band region, then electron may finally beak free from the surface of solid. We call this energy level Work function. It's defined as minimum thermodynamic work (or energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" means that the final electron position is far from the surface on the atomic scale, but still too close to the solid to be influenced by ambient electric fields in the vacuum. The work function is not a characteristic of a bulk material, but rather a property of the surface of the material (depending on crystal face and contamination). Work function of most of the metals is around 4eV. Silicon W=4.7eV

W = -eø - Ef (e=charge of electron, ø = electrostatic potential in the vacuum nearby the surface, so -eø represents the energy of electron near the surface)

If we charged a material to V volts, then V=-Ef/e. Rearranging above eqn, ø = -Ef/e - W/e = V - W/e. So, potential near surface of any material in vacuum is less than the potential applied by an amount equal to Work function potential (work function divided by e). This means that if 2 conductors are kept at same potential by shorting to each other, but if their work function are different, then their surface potential will be different. So, there will be an electric field in vacuum going from surface of 1 metal to other metal. This is used to get electrons flowing in vacuum tube filaments or in electron guns.

Work function is very important in solid state physics, as work function of different material control how electrons flow when different materials are put in contact.

It is also important in photo electric emission, where it determines the minimum photon energy required to liberate an electron from a substance. Energy beyond fermi level gets the electron right on the surface of material ready to escape. So, light of frequecy f has energy=hf, which when exceeds workfunction of material will liberate an electron from it.

Reduction Potential (W)

As we move higher up in energy band (in conduction band), electrons become more free to move around, but still within the solid material. If we go much higher than conduction band region, then electron may finally beak free from the surface of solid. We call this energy level Work function. It's defined as minimum thermodynamic work (or energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface. Here "immediately" means that the final electron position is far from the surface on the atomic scale, but still too close to the solid to be influenced by ambient electric fields in the vacuum. The work function is not a characteristic of a bulk

Link => https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_Structure_and_Reactivity_in_Organic_Biological_and_Inorganic_Chemistry_(Schaller)/V%3A__Reactivity_in_Organic_Biological_and_Inorganic_Chemistry_3/01%3A_Reduction_and_Oxidation_Reactions/1.03%3A_Reduction_Potential