Chemical Engineering Thermodynamics - Chapter 1

Chemical Engineering Thermodynamics - Chapter 1: Introduction

• Thermodynamics explores the relationships between heat and various energy forms.
• Chemical Engineering Thermodynamics applies these principles to both chemical and physical processes.

Dimensions and Units

• Dimensions are foundational concepts, that include mass (M), length (L), time (t), and temperature (T).
• Units are used to express dimensions, for example, grams (g) for mass.
• The SI System is grounded in meter, kilogram, second, ampere, Kelvin, candela, and mole values.
• Derived Units come from basic units (e.g., Newton ($N = kg \cdot m/s^2$)).

Measures of Amount or Size

• Mass (m) denotes the quantity of matter.
• Volume (V) describes the space occupied.
• Mole (mol) represents the substance amount containing as many elementary entities as there are atoms in 0.012 kg of carbon-12.

Force

• Newton's Second Law defines force as $F = ma$ (F = force, m = mass, a = acceleration).
• Weight is the force exerted on an object because of gravity ($g \approx 9.8 m/s^2$).

Temperature

• Celsius Scale is based on water's freezing (0°C) and boiling (100°C) points.
• Kelvin Scale is an absolute temperature scale where 0 K is absolute zero; $T(K) = t(°C) + 273.15$.
• Rankine Scale is an English absolute temperature scale; $T(°R) = t(°F) + 459.67$.
• Fahrenheit Scale: $T(°F) = 1.8t(°C) + 32$.

Pressure

• Pressure is defined as force per unit area; $P = F/A$.
• Common pressure units include Pascals (Pa).
• Atmospheric Pressure is the pressure exerted by the atmosphere.
• Gauge Pressure is pressure relative to atmospheric pressure.
• Absolute Pressure represents the total pressure, adding atmospheric pressure into the equation.

Work

• Work occurs when energy is transferred upon force acting via a distance.
• Mechanical Work is calculated as $W = F \cdot d$ (F = force, d = distance).
• PV Work occurs during system expansion or compression; $W = \int P dV$.

Energy

• Kinetic Energy (KE) is energy due to motion; $KE = \frac{1}{2}mv^2$.
• Potential Energy (PE) is energy due to position; $PE = mgh$.
• Internal Energy (U) is energy linked to a system's molecular structure and activity.
• Total Energy (E) sums kinetic, potential, and internal energies; $E = KE + PE + U$.

Heat

• Heat is the energy transferred because of temperature difference.
• Units of heat include Joules (J).
• Specific Heat Capacity (c) denotes heat to raise unit mass temperature by one degree.
• Heat Transfer represents transit energy because of a temperature difference.

The State Postulate

• Simple Compressible System: The state is fully defined by two independent, intensive properties.
• State Postulate: For a simple compressible system, two independent intensive properties fully define its state .

Equilibrium

• Thermodynamic Equilibrium occurs when a system's properties are uniform and unchanging, with thermal, mechanical, phase, and chemical equilibrium.

The Phase Rule

• Gibbs Phase Rule: $F = 2 - \pi + N$ (F = degrees of freedom, $\pi$ = number of phases, N = number of chemical species).
• Degrees of Freedom is the number of intensive variables independently changed without changing the phases number.

The Reversible Process

• A Reversible Process is one that can be reversed without impacting the surroundings.
• It's Infinitesimally slow, series of equilibrium states.
• Serves as idealization for thermodynamic analysis.

Constant-V and Constant-P Processes

• Constant-Volume Process (Isochoric): Volume remains constant; $W = 0$.
• Constant-Pressure Process (Isobaric): Pressure remains constant; $W = P\Delta V$.

Enthalpy

• Enthalpy is a thermodynamic property defined as $H = U + PV$.
• Helpful for analyzing constant-pressure processes.

Heat Capacity

• Heat Capacity represents required heat to change a substance's temperature by one degree.
• Specific Heat at Constant Volume ($C_v$): $(\frac{\partial U}{\partial T})_v$.
• Specific Heat at Constant Pressure ($C_p$): $(\frac{\partial H}{\partial T})_p$.
• Relationship: $C_p = C_v + R$ (for ideal gases).

Process Equipment

• Process Equipment examples span heat exchangers, reactors, distillation columns.
• Facilitating chemical and physical processes.

Thermodynamics and the Conservation Laws

• Conservation of Mass: Mass is not created or destroyed.
• Conservation of Energy (First Law of Thermodynamics): Energy can only be converted; $\Delta U = Q - W$.
• Second Law of Thermodynamics: Total system entropy can only increase or remain constant ideally.
• Third Law of Thermodynamics: Perfect crystal entropy at absolute zero is zero.

Engineering Problem Solving

• Define problem, gather information, develop a solution plan, execute, evaluate.

Computer Programs

• Use software for thermodynamic calculations and simulations.
• Aspen Plus is an example of this
• Applications include process design and more.

Chapter 14: Pricing Strategies

• Price is the monetary charge for a product or service.
• Sum of all values customers sacrifice gaining product/service benefits.

Price = value

• Prices are based on the price and perceived benefit, essentially the customer is willing to pay a price for a product or service if they are of equal value.

Factors to Consider When Setting Prices

• Customer Perceptions of Value determines price ceiling.
• Product Costs dictate the price floor.
• Marketing strategy, objectives, and the market's characteristics are all external considerations to take into account when determining prices.

Customer Value-Based Pricing

• Pricing is determined in two ways i.e. good-value pricing approach where a fair price is set for the given benefits and value-added pricing strategy, which is enhancing features and services to support higher prices.

Cost-Based Pricing

• Fixed costs do not fluctuate with production or sales revenue.
• Variable costs change directly with the production level.
• Total costs are the sum of fixed and variable costs for a given production level.

Cost-Plus Pricing

• Applying a standard markup on the product's cost.

Break-Even Pricing (& Target Profit Pricing)

• Setting a price that covers the costs of production and marketing, or to achieve a desired profit.

Competition-Based Pricing

• Going-rate pricing: setting prices based largely on competitors' prices
• Sealed-bid pricing - Based on how ones believes competitors will price, rather than on actual analysis of internal costs or demand

Overall Marketing Strategy, Objectives, and Mix

• Prices can aid numerous goals: survival, current profit maximization.
• Achieving market share leadership
• Sustaining product quality leadership

Organizational Considerations

• Small companies let upper management set the prices for their products of services.
• Large companies will often get their divisional or product managers involved

The Market and Demand

• Pricing varies across market types (such as in a pure market or monopolistic market).
• Pure market - Sellers do not expend much effort to competitively marketing their commodities since the product is homogenous.
• Monopolistic market - a competitive strategy adopted to help highlight non-price differences

Analyzing the Price-Demand Relationship

• The demand curve exhibits price's influence on product quantity sold.
• Price elasticity evaluates consumer demand's sensitivity to price changes.

The Economy

• Economic factors (boom/recession) drastically shape the pricing strategies

Pricing Decisions

• Price skimming charges those who are willing to pay the most initially, while marketing penetration sets low to quickly penetrate fast.

Product Mix Pricing Strategies

• Product line pricing prices various products within product lines.
• Optional-product pricing offers add-ons and accessories with main product.
• Captive-product pricing, companies will sell a product low, and make their money from associated products
• By-product pricing prices by-products to make associated products more competitive.
• Product bundle combines products together to sell at a reduced price

Price Adjustment Strategies

• The major price adjustment strategies are discounts, segmented pricing, psychological, or promotional pricing.

Price Changes

• Price cuts can start due to reduced capacity or falling demand in an attempt to dominate the market.
• Initiating price increases is for products facing cost inflation or excess demands

Buyer Reactions to Price Changes

• Buyer reactions determine the quality or value they place on a product.

Competitor Reactions to Price Change

• Competitors can either cut or raise prices with their products in retaliation to a rival company

Public Policy and Pricing

• Pricing should be done to ensure compliance with relevant laws.
• Price-fixing - agreement between competitor to set market prices; anti-competitive pricing across channel levels
• Price discrimination - Selling the same products to different stores at different prices
• Price maintenance - a manufacturer imposes resale price restrictions on retailers.

Heat Transfer

• Heat transfer refers to the exchange of thermal energy between physical systems depending on temperature and pressure, dissipating heat is one of the critical things to consider

Modes of Heat Transfer

• Heat transfer operates in three different modes i.e. conduction, convection, and radiation

Conduction

• Conductive heat transfer happens in solids or fixed fluids due to unequal temperature gradient.

Fourier's Law

• Mathematical expression of heat conduction (q" = -kdT/dx), where thermal conductivity determines the heat amount transferred over distance.
• Where:
  • $q''$ = the heat flux $(\frac{W}{m^2})$
  • $k$ = the thermal conductivity $(\frac{W}{m \cdot K})$ -$\frac{dT}{dx}$ = the temperature gradient $(\frac{K}{m})$

Convection

• Convection transfers heat between a surface with a moving fluid due to temperature variance.

Newton's Law of Cooling

• Mathematical Expression of Convection (q" = h(Ts - T∞)), where heat flux depends on the surface and fluid temperature.
  • $h$ = is the convection heat transfer coefficient $(\frac{W}{m^2 \cdot K})$
  • $T_s$ = is the surface temperature $(K)$
  • $T_{\infty}$ = is the fluid temperature $(K)$

Radiation

• Radiation is the net transfer of heat between two surfaces using electromagnetic waves.

Stefan-Boltzmann Law

• Mathematical expression of Radiation (q" = εσ(Ts4 - Tsurr4)), where heat flux emitted from surface depends on surroundings.
  • $\epsilon$ = is the emissivity of the surface (dimensionless)
  • $\sigma$ = is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \frac{W}{m^2 \cdot K^4}$)
  • $T_s$ = is the surface temperature $(K)$
  • $T_{surr}$ = is the surrounding temperature $(K)$

Thermal Resistance

• Thermal resistance refers to a material's ability to resist flow

Conduction Resistance

$R_{cond} = \frac{L}{kA}$ where

• L is the thickness of the material (m)
• k is the thermal conductivity of the material $(\frac{W}{m \cdot K})$
• A is the area normal to the direction of heat transfer $(m^2)$

Convection Resistance

$R_{conv} = \frac{1}{hA}$ where

• h is the convection heat transfer coefficient $(\frac{W}{m^2 \cdot K})$
• A is the area exposed to the fluid $(m^2)$

Radiation Resistance

$R_{rad} = \frac{1}{h_{rad}A}$ where

$h_{rad} = \epsilon \sigma (T_s + T_{surr})(T_s^2 + T_{surr}^2)$

• $\epsilon$ is the emissivity of the surface (dimensionless)
• $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \frac{W}{m^2 \cdot K^4}$)
• $T_s$ is the surface temperature (K)
• $T_{surr}$ is the surrounding temperature (K)
• A is the area of the surface $(m^2)$

Total Resistance

• Calculate by either adding the resistance in series/parallel by:

For series resistances: $\qquad R_{total} = R_1 + R_2 + R_3 +...$

For parallel resistances: $\qquad \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} +...$

Heat Transfer Rate

$\qquad q = \frac{T_1 - T_2}{R_{total}}$ where

• $T_1$ and $T_2$ are the temperatures at the two ends of the thermal resistance (K)
• $R_{total}$ is the total thermal resistance between the two points $(\frac{K}{W})$

Fin Efficiency

$\qquad \eta_{fin} = \frac{q_{actual}}{q_{max}}$

$q_{max} = hA_{fin}(T_b - T_{\infty})$ where

• $q_{actual}$ is the actual heat transfer rate from the fin (W)
• $q_{max}$ is the ideal heat transfer rate from the fin (W)
• h is the convection heat transfer coefficient $(\frac{W}{m^2 \cdot K})$
• $A_{fin}$ is the surface area of the fin $(m^2)$
• $T_b$ is the base temperature of the fin (K)
• $T_{\infty}$ is the fluid temperature (K)

Overall Heat Transfer Coefficient

$\qquad U = \frac{1}{A R_{total}}$ where

• U is the overall heat transfer coefficient $(\frac{W}{m^2 \cdot K})$
• A is the area normal to the direction of heat transfer $(m^2)$
• $R_{total}$ is the total thermal resistance $(\frac{K}{W})$

The dot product

• The Dot product is the sum of multiple vectors $ \qquad \vec{a} \cdot \vec{b} = a_1b_1 + a_2b_2 $
• Example:*

$ \cdot = 2(3) + 4(-1) = 6 - 4 = 2$

$ \cdot = (-1)(\frac{1}{2}) + (7)(-2) = -\frac{1}{2} - 14 = -\frac{29}{2}$

Properties of the Dot Product

• For vectors and scalars

$\qquad \vec{a} \cdot \vec{a} = |\vec{a}|^2$

$\qquad \vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}$

$\qquad \vec{a} \cdot (\vec{b} + \vec{c}) = \vec{a} \cdot \vec{b} + \vec{a} \cdot \vec{c}$

$\qquad (k\vec{a}) \cdot \vec{b} = k (\vec{a} \cdot \vec{b}) = \vec{a} \cdot (k\vec{b})$

$\qquad \vec{0} \cdot \vec{a} = 0$

Angle between vectors

• the angle between two vectors is defined by

$\qquad \cos{\theta} = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|}$

Orthogonal vectors

• Orthogonal vectors are found when: $\qquad \vec{a} \cdot \vec{b} = 0$.