"Sometimes the best helping hand you can get is a good, firm push."

3rd Law of Thermodynamics Absolute (T=0 K) S is 0 for all perfect crystalline substances Thus the absolute S of a gas at temperature T is: Example: The Third Law of Thermodynamics can be visualized by thinking about water. Water in gas form has molecules that can move around very freely. Water vapor has very high entropy (randomness). As the gas cools, it becomes liquid. The liquid water molecules can still move around, but not as freely. They have lost some entropy. When the water cools further, it becomes solid ice. The solid water molecules can no longer move freely, but can only vibrate within the ice crystals. The entropy is now very low. As the water is cooled more, closer and closer to absolute zero, the vibration of the molecules diminishes. If the solid water reached absolute zero, all molecular motion would stop completely. At this point, the water would have no entropy (randomness) at all.

Microscopic Point of View: Entropy is the measure of molecular disorder or randomness. As a system becomes more disordered, the position of the molecules becomes less predictable and the entropy increases. Entropy is the lowest in a solid because molecules are held in place and simply vibrate and highest in a gas where the molecules are free to move in any direction. Entropy of a pure crystalline substance at absolute zero temperature is zero since the state of each molecule is known  Third Law of Thermodynamics

Chapter 4 Heat Effects

Importance in the Industry Heat Transfer is a common operation in the chemical industry Catalytic oxidation reaction is most effective when carried out a temperatures near 2500C. The preheater design depends on the rate of heat transfer

Sensible Heat Effects Constant-volume process U independent of volume (Ideal gases, incompressible fluids, low pressure gases)

For mechanical reversible constant volume process

Sensible heat effects dU = Cv dT dH = Cp dT For mechanically reversible, constant pressure, closed system and for steady flow systems where Ep=Ek=0, Independent of P but dependent on T

Temperature dependence of the heat capacity Where constants A, B,…are constant characteristics of the particular substance Heat capacities for real gases are only slightly different, except at high pressures. Values of the constants can be found in Append. C1.

Example 4.1 The parameters listed in Table C.1 require use of Kelvin temperature in Eq. 4.4. Equations of the same form may also be developed for use with temperatures in 0C, R and 0F, but the parameter values are different. Develop an equation for Cpig/R for temperatures in 0C.

Evaluation of the Sensible-Heat The calculation of Q or H is straightforward given To and T By use of computer program : 2. By Evaluation of the integral :

Evaluation of the sensible heat integration If T is known and to determine H and Q Equation 4.7

If H or Q is known but not the final T: Factoring (t -1) from previous equation,

Mean heat capacity

Gas mixtures

Use of defined functions: definitions by textbook for computer calculations From eq 4.7 From eq 4.8

Calculate the heat required to raise 1 mol of CH4 from 260 to 600oC in a steady flow process at a pressure sufficiently low that methane may be considered an ideal gas Refer App C1 for data, Eq 4.7

Example 4.1 page 150 For steady flow in a heat exchanger at approximately atmospheric pressure, what is the heat transfered (b) When 12 mole of propane I heated from 250 to 1200C

Eq 4.8

Latent heat of pure substances (vaporization and fusion) Clapeyron equation: During phase change constant P and no change in T, heat used for phase change

Heat of Reaction Clapeyron equation: Heat of Reaction (ΔHr ) - Heat flow (Q) in a reaction at constant pressure is equal to the change in enthalpy for the reaction Clapeyron equation: General reaction: Stoichiometric coefficients are negative for reactants and positive for products. Enthalpy change for the amount of reaction indicated by the stoichiometric coefficients, at 298 K and with the species all in their standard states (at 1 atm).

Standard heat of Formation is given in Appendix C

Heat of Reaction Problem Calculate the heat of reaction at standard conditions for the following reaction:

Solution to Heat of Reaction Problem

Consider this reaction: CO2 (g) + H2 (g)  CO (g) + H20(g) at 25oC Evaluating the heat of reaction:

Heat of Combustion The amount of heat liberated when a combustible material like fuel is burned A chemical process of liberating heat by oxidizing the reactant (usually termed as fuel) to produce CO2 and water The standard heat of combustion, DHc0, is based on the oxidation of the compound to CO2, H2O, HCl(l), etc. The reference conditions are 25ºC and 1 atm and refers to 1 mol of substance burned. The relationship between heat of reaction and heat of combustion:

Sample Problem on Combustion Compute the standard heat of formation of a liquid n-pentane (C5H12) on the assumption of complete combustion

Illustrative Problem 4.24/154 Natural gas (assume pure methane) is delivered to a city via pipeline at a volumetric rate of 150 million standard cubic feet per day. If the selling price is $5 per GJ of higher heating value (HHV), what is the expected revenue in dollars per day ? Standard conditions are 600F and 1 atm.

HHV (Higher Heating Value) of a fuel is its standard heat of combustion at 250C with liquid water as a product. The higher heating value is the negative of the heat combustion with water as the liquid product

Group Seat Work 4.44 page 157 A propane-fired water delivers 80% of the standard heat of combustion of the propane [at 250C with CO2 (g) and H20(g) as products] to the water. If the price of the propane is $2.20 per gallon as measured at 250C, what is the heating cost in $ per million BTU ( V= 89.373 cm3/mol(

Heats of Reaction in the First Law Consider a steady-state flow process, with negligible kinetic and potential energies and no shaft work. Include heat of reaction in the enthalpy difference. Divide general 1st Law by mass. The first term represents the enthalpy of the product stream above the standard state. The second term is the heat of reaction in the standard state. The third term represents the enthalpy of the reactant stream above the standard state.

Heat of Reaction at Non-Standard Conditions [DHrxn(T)]

Temperature dependence on DH (II)

Use of defined functions: definitions by textbook for computer calculations

Calculate the standard heat of the methanol synthesis reaction at 800oC: CO(g) + 2H2 (g)  CH3OH

Problem 4.51 page 158 A natural-gas fuel contains 85 mol% methane, 10 mol% ethane, and 5 mol% nitrogen. (a) What is the standard heat of combustion (KJ/mol) of the fuel at 250C with H20 (g) as a product? (b) The fuel is supplied to a furnace with 50% excess air, both entering at 250C. The products leave at 6000C. If the combustion is complete and if no side reactions occur, how much heat (KJ/mol of fuel ) is transferred in the furnace.

4.34 page 156 The gas stream from a sulfur burner consists of 15 mol % SO2, 20 mol % O2 and 65mol %N2. The gas stream atmospheric pressure and 4000c enters a catalytic converter where 86% of the SO2 is further oxidized to SO3. On the basis of 1 mol of gas entering, how much heat must be removed from the converter so that the product gases leave at 5000C

4.37 page 156 An equimolar mixture of Nitrogen and acetylene enters a steady-flow reactor at 250C and atmospheric pressure. The only reaction occuring is N2 (g) + C2H2 = 2HCN (g). The product gases leave the reactor at 6000C and contain 24.2 mol% HCN. How much heat is supplied to the reactor per mole of product gas ?