CHE 201 Engineering Thermodynamics Notes PDF

DEPARTMENT OF CHEMICAL ENGINEERING, FACULTY OF TECHNOLOGY OBAFEMI AWOLOWO UNIVERSITY, ILE IFE CHE 201: ENGINEERING THERMODYNAMICS MODULE 2: FIRST LAW OF THERMODYNAMICS 1: ENERGY, HEAT AND WORK 2023/2024 SESSI...

DEPARTMENT OF CHEMICAL ENGINEERING, FACULTY OF TECHNOLOGY OBAFEMI AWOLOWO UNIVERSITY, ILE IFE CHE 201: ENGINEERING THERMODYNAMICS MODULE 2: FIRST LAW OF THERMODYNAMICS 1: ENERGY, HEAT AND WORK 2023/2024 SESSION Lecturer: SANDA, O. Ph.D. Chem. Eng.(Ife). Reg. Engr. (COREN),  1. INTRODUCTION TO THERMODYNAMICS – a recap….. The term thermodynamics originates from two Greek words: thermos, meaning "heat," and dynamis, meaning "power." At its core, thermodynamics is the study of energy—how it is converted, transferred, and how it governs the behavior of systems. For engineers, thermodynamics is crucial because it provides the foundation for understanding and designing systems like engines, power plants, refrigerators, and air conditioners. Engineering thermodynamics specifically focuses on the principles and laws that govern the conversion of heat into work and vice versa. It explores the relationships between thermal, mechanical, and chemical processes, enabling us to analyze and optimize the performance of machines and systems under various conditions. What is Thermodynamics? Thermodynamics is the branch of science that deals with: 1. Heat and Work: How these forms of energy interact with matter. 2. Energy Conversion: The transformation of energy from one form to another, such as from chemical energy in fuel to mechanical energy in an engine. 3. The Direction of Change: Understanding why and how systems evolve over time, guided by natural laws. In simpler terms, thermodynamics helps answer questions like:  How does a car engine convert fuel into motion?  Why does heat flow from hot objects to cold objects?  What limits the efficiency of energy conversion? 1.1 THERMODYNAMIC LAWS: THE FRAMEWORK The principles of thermodynamics are based on experimental observations and are summarized in four fundamental laws: 1. Zeroth Law of Thermodynamics: Thermal Equilibrium and Temperature Measurement  If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.  This law forms the basis for temperature measurement and establishes that temperature is a measurable property. Example: A thermometer reaches thermal equilibrium with a body and accurately measures its temperature. 2. First Law of Thermodynamics: Energy Conservation  Energy cannot be created or destroyed; it can only be transformed from one form to another.  This law introduces the concept of internal energy, which is the energy contained within a system. Mathematical Formulation: 𝛥𝑈 = 𝑄 − 𝑊 Where:  ΔU: Change in internal energy  Q: Heat added to the system  W: Work done by the system Example: In a steam engine, heat energy from burning fuel is partly converted into work to move pistons. 3. Second Law of Thermodynamics: Limits of Energy Conversion and Entropy  Not all heat can be converted into work. This law introduces the concept of entropy, which measures the degree of disorder in a system.  The second law determines the direction of processes and whether they are feasible. Key Implication: Heat flows naturally from a hot body to a cold body, not the other way around. Example: In refrigerators, work is done to transfer heat from a cold interior to the warmer surroundings. 4. Third Law of Thermodynamics: Absolute Zero and Entropy  The entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero (0 K). Example: At absolute zero, molecular motion ceases, and the system is in its lowest energy state. Applications of Thermodynamics  Heat Engines: Devices that convert heat into mechanical work, such as car engines and turbines.  Refrigeration: Systems that transfer heat from cooler regions to warmer regions, essential in food preservation and air conditioning.  Power Plants: Facilities that generate electricity using thermodynamic cycles like the Rankine and Brayton cycles.  1.2. THERMODYNAMIC SYSTEMS One of the foundational concepts in thermodynamics is the system. A system refers to the portion of the universe chosen for analysis. Everything external to this system is called the surroundings, and the system is separated from its surroundings by a boundary, which may be real or imaginary. This boundary defines the region of interest and facilitates analysis. Key definitions:  Thermodynamic system: A specific quantity of fixed mass or defined space chosen for study.  Surroundings: Everything outside the system.  Boundary: The interface separating the system and its surroundings. This boundary may allow for the transfer of energy and/or matter.  Universe: The system and surroundings together form the universe. Interactions Between System and Surroundings Systems interact with their surroundings through exchanges of energy or matter across the boundary. These interactions can include: 1. Energy exchange: Heat, work, radiation, friction, etc. 2. Mass exchange: Movement of matter across the boundary. Types of Thermodynamic Systems Thermodynamic systems are classified based on their ability to exchange energy or matter with their surroundings: 1. Closed System: A system where no matter can cross the boundary, but energy can be exchanged (e.g., heat, work). An example of a closed system is a sealed piston-cylinder device where gas expands and contracts without matter entering or leaving. 2. Open System: A system where both matter and energy can cross the boundary. A typical example of an open system is a steam turbine or a water pump, where fluids flow in and out while work and heat are exchanged. 3. Isolated System: A system that does not exchange either matter or energy with its surroundings. A typical example is a thermos flask with an ideal seal. 4. Adiabatic System: A system that does not allow heat transfer across its boundary but may exchange work. A typical example of an adiabatic system is a well-insulated piston-cylinder device. 5. Diathermic System: A system where heat can cross the boundary freely, but other forms of exchange may be restricted. A classic example of a diathermic system is a metal container allowing heat transfer with the environment.  1.3. THERMODYNAMIC PROCESSES A process is the transformation that a thermodynamic system undergoes as it changes from an initial state to a final state. The path taken by the system during this transformation is of key importance.  Actual process: Occurs when the system deviates from thermodynamic equilibrium during the process.  Ideal process: Assumes an infinitesimally small deviation from equilibrium, such that every intermediate state can be treated as an equilibrium state (quasi-equilibrium). Key Types of Processes The prefix "iso-" denotes a property that remains constant during the process:  Isobaric Process: Pressure remains constant.  Isochoric Process: Volume remains constant.  Isothermal Process: Temperature remains constant.  Adiabatic Process: No heat transfer occurs across the boundary.  Cyclic Process: The system returns to its initial state after completing the process (ΔU=0). Reversible vs. Irreversible Processes 1. Reversible Process: o A process that can be reversed without leaving any changes in the system or surroundings. o In theory, reversible processes proceed infinitely slowly, maintaining thermodynamic equilibrium at all stages. o Examples:  Frictionless relative motion  Expansion and compression of spring  Frictionless adiabatic expansion or compression of fluid  Polytropic expansion or compression of fluid  Isothermal expansion or compression  2. Irreversible Process: o A process that cannot be reversed to restore both the system and surroundings to their initial states. o Most real-world processes are irreversible due to factors such as friction, unrestrained expansion, or heat transfer across finite temperature differences. Characteristics of Reversible Processes 1. The system passes through the same equilibrium states in reverse order. 2. Leaves no lasting effects or history in the surroundings. 3. Must involve a continuous series of equilibrium states.  2. ENERGY, WORK, AND HEAT In thermodynamics, understanding the concepts of energy, work, and heat is fundamental for analyzing and designing engineering systems. This section breaks down these concepts and their roles in thermodynamic processes. 2.1. ENERGY Energy is a broad term encompassing both stored energy and energy in transition. It is the capacity of a system to perform work or produce change. Energy manifests in various forms, each with distinct characteristics and implications for thermodynamic analysis. Types of Energy 1. Stored Energy: Energy possessed by a substance due to its state or position. o Mechanical Energy: Includes:  Potential Energy (PE): Energy due to position in a gravitational field, calculated as: 𝑷𝑬 = 𝒎𝒈𝒉 where m is mass, g is gravitational acceleration, and h is height above a reference point.  Kinetic Energy (KE): Energy due to motion, calculated as: 𝟏 𝑲𝑬 = 𝒎𝒗𝟐 𝟐 where m is mass and v is velocity. o Internal Energy (U): Energy associated with the microscopic state of a system, including:  Molecular motion (translational, rotational, vibrational).  Intermolecular forces. o Other Forms of Stored Energy:  Chemical Energy: Energy stored in molecular bonds.   Electrical Energy: Energy due to electric fields or charges. 2. Energy in Transition: Energy crossing the system boundary, manifesting as: o Heat (Q): Energy transfer due to temperature difference. o Work (W): Energy transfer due to mechanical or other external influences. 2.2. STORED ENERGY IN NON-FLOW AND FLOW PROCESSES  Non-Flow Processes: In processes where the system is stationary, changes in kinetic energy (KE) and potential energy (PE) are typically negligible. The primary focus is on changes in internal energy (ΔU).  Flow Processes: When mass flows across the system boundary, changes in both kinetic energy and potential energy must be considered alongside changes in internal energy. The total change in stored energy is given by: 𝜟𝑬 = 𝜟𝑼 + 𝜟𝑲𝑬 + 𝜟𝑷𝑬 Heat and Work: Energy in Transition Unlike stored energy, heat and work are transient forms of energy. They are the only means by which energy can cross the boundary of a system. 1. Heat (Q): Heat is energy transfer due to a temperature difference between the system and its surroundings. o Key Characteristics:  Heat always flows from high to low temperature (Second Law of Thermodynamics).  It is a path-dependent quantity and not a state property. 2. Work (W): Work is energy transfer resulting from force applied across a distance or from other forms of interaction (e.g., electrical work). o Key Characteristics:  Like heat, work is also a path-dependent quantity and not a state property.  Common examples in thermodynamic systems include:   Boundary Work: Expansion or compression of a gas.  Electrical Work: Energy transfer due to current flow. Note: Heat and Work are Not Stored Energy. These forms of energy exist only during the transition or interaction between a system and its surroundings. Once the energy is transferred, it contributes to stored energy in the system (e.g., increasing internal energy). 2.3. ENERGY CONSERVATION IN THERMODYNAMICS The First Law of Thermodynamics governs the interplay between energy forms, stating that energy cannot be created or destroyed, only transferred or transformed. For a thermodynamic system: 𝜟𝑬 = 𝑸 − 𝑾 Where:  ΔE: Change in total stored energy.  Q: Heat added to the system.  W: Work done by the system. This equation may also be written in differential form: 𝒅𝑬 = 𝑸̇ − 𝑾̇ 𝒅𝒕 Sign Convention in Thermodynamics Understanding the sign convention for heat and work is essential for consistent analysis of thermodynamic processes. The conventions help define whether energy is being added to or removed from a system. Work (W) 1. Positive Work (+W): Work is positive when the system does work on its surroundings. A typical example is the pushing a piston outward in an engine cylinder due to fluid expansion. 2. Negative Work (−W): Work is negative when work is done on the system by the surroundings. A typical example of negative work is when a piston is compressed by an external force or a handle is rotated to transfer energy into the system. Heat (Q) 1. Positive Heat (+Q): Heat is positive when it flows into the system from the surroundings. A typical example of positive heat flow is the heating a gas in a closed cylinder, causing its temperature and internal energy to increase. 2. Negative Heat (−Q): Heat is negative when it flows out of the system into the surroundings. A typical example is the cooling a system, where heat is rejected to the surroundings. Summary Table of Sign Conventions Energy Interaction Sign Direction of Energy Flow Work done by the system +W Energy leaves the system as work output. Work done on the system −W Energy enters the system as work input. Heat added to the system +Q Energy enters the system as heat input. Heat removed from the system −Q Energy leaves the system as heat output. WORK IN THERMODYNAMICS In thermodynamics, work refers to energy transfer that occurs when a force is applied, causing a displacement. Work is a key concept for analyzing energy interactions in engineering systems. Definition of Work in Mechanics In basic mechanics, work is defined as the product of force and displacement in the direction of the force: 𝑊 =𝐹⋅𝑠 Where:  W: Work (Joules)  F: Force (Newtons)  s: Displacement in the direction of the force (meters) Work in a Thermodynamic System Consider a system with a gas enclosed in a cylinder fitted with a movable piston. The work done depends on whether the gas expands or contracts: 1. Expansion Work: When the gas expands, it pushes the piston outward. In this case, work is done by the system on the surroundings. 2. Compression Work: When the gas contracts, the surroundings push the piston inward. Here, work is done on the system by the surroundings. Work Done by a Gas: Mathematical Formulation The force exerted by the gas on the piston is related to pressure and area: 𝑭=𝑷⋅𝑨 Where:  P: Pressure exerted by the gas (Pa)  A: Cross-sectional area of the piston (m²) The work done, W, during a small displacement ds is: 𝒅𝑾 = 𝑭 ⋅ 𝒅𝒔 Substituting 𝑭 = 𝑷 ⋅ 𝑨 and recognizing that 𝑨 ⋅ 𝒅𝒔 = 𝒅𝑽 (where dV is the small change in volume): 𝒅𝑾 = 𝑷 ⋅ 𝒅𝑽 To calculate the total work done as the gas expands or contracts, integrate over the volume change: 𝑽𝟐 𝑾 = ∫ 𝒑 𝒅𝑽 𝑽𝟏 Where:  V1: Initial volume  V2: Final volume  P: Pressure, which may vary during the process Based on this, we can say that work is simply the area under the P – V curve Types of Work in Thermodynamics 1. Isobaric Process (Constant Pressure): If the pressure remains constant, the work done simplifies to: 𝑾 = 𝑷(𝑽𝟐 − 𝑽𝟏 ) 2. Isochoric Process (Constant Volume): No volume change occurs, so 𝑾 = 𝟎 3. Isothermal Process (Constant Temperature): For an ideal gas undergoing an isothermal process, we can say that the relation between P and V is defined by: 𝑷𝑽 = 𝒏𝑹𝑻 𝒏𝑹𝑻 Or 𝑷 = 𝑽 PV = constant Where n = number of moles of gas, R is the universal gas constant, and T is the Temperature (in Kelvin). From here, we have: 𝑽𝟐 𝟏 𝑾 = 𝒏𝑹𝑻 ∫ 𝒅𝑽 𝑽 𝑽𝟏 Which gives: 𝑽𝟐 𝑾 = 𝒏𝑹𝑻 𝐥𝐧 ( ) 𝑽𝟏 4. Polytropic Process: The work depends on the pressure-volume relationship governed by the adiabatic equation: PVn=constant:  PVn = constant The work done for a polytropic process is given by: 𝑷 𝟏 𝑽𝟏 − 𝑷 𝟐 𝑽𝟐 𝑾= 𝒏−𝟏 Where 𝑛 ≠ 1. 5. Adiabatic Process (No Heat Transfer): This is a special case of polytropic processes where 𝑷𝑽𝜸 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 Where γ is the ratio of specific heats. Here’s a summary P – V diagram for the various processes: HEAT TRANSFER IN THERMODYNAMIC PROCESSES Let’s begin by introducing a new quantity known as ENTHALPY (H), such that: 𝑯 = 𝑼 + 𝑷𝑽 Heat transfer depends on the type of thermodynamic process: 1. Isobaric Process (Constant Pressure): Heat transfer changes the internal energy and performs work on or by the system: 𝑸 = 𝜟𝑯 = 𝒎𝑪𝒑 𝜟𝑻 where cp is the specific heat capacity at constant pressure 2. Isochoric Process (Constant Volume): No work is done, so heat transfer only changes the internal energy 𝑸 = 𝜟𝑼 = 𝒎𝑪𝒗 𝜟𝑻 where cv is the specific heat capacity at constant volume 3. Isothermal Process (Constant Temperature): Heat transfer occurs while the internal energy remains constant, and work is done by or on the system. 4. Adiabatic Process (No Heat Transfer): There is no heat exchange (Q=0), and changes in internal energy are due entirely to work. For an ideal gas, the relationship between pressure and volume is given by: 𝑷𝑽 = 𝒎𝑹𝑻 Expressing the enthalpy relation in a differential form, we have: 𝑑𝐻 = 𝑑𝑈 + 𝑑(𝑃𝑉) Or, 𝒎𝑪𝒑 𝒅𝑻 = 𝒎𝑪𝒗 𝒅𝑻 + 𝑑(𝑚𝑅𝑇) This can be simplified to give: 𝑪𝒑 = 𝑪𝒗 + 𝑹 𝐶𝑝 Note that 𝐶𝑝 > 𝐶𝑣. If we define the ratio of the specific heats as 𝛾 = , we have: 𝐶𝑣 𝛾𝑅 𝐶𝑝 = 𝛾−1 and 𝑅 𝐶𝑣 = 𝛾−1 Solved Examples 1. 0.25 kg of a gas contained within a piston–cylinder assembly undergoes a constant-pressure process at 5 bar beginning at v1 = 0.20 m3/kg. For the gas as the system, the work is -15 kJ. Determine the final volume of the gas, in m3. Solution Given: Mass of the gas, m = 0.25 kg, v1 = 0.20 m3/kg, P = 5 bar, W = -15kJ (or – 15,000 J) Thus, we have: 105 𝑁/𝑚2 System pressure, 𝑃 = 5 𝑏𝑎𝑟 [ ] = 𝟓 × 𝟏𝟎𝟓 𝑵/𝒎𝟐 1 𝑏𝑎𝑟 𝑚3 Initial pressure, 𝑉1 = 0.25 𝑘𝑔 × 0.20 𝑘𝑔 = 𝟎. 𝟎𝟓 𝒎𝟑 Final pressure, 𝑉2 is not known. For a constant pressure system, the work done is: 𝑊 = 𝑃(𝑉2 − 𝑉1 ) Or 𝑊 −15000 𝐽 𝑉2 = + 𝑉1 = + 0.05 𝑚3 = 𝟎. 𝟎𝟐 𝒎𝟑 𝑃 5 × 105 𝑁/𝑚2 2. A gas is compressed from V1 = 0.3 m3, P1 = 1 bar to V2 = 0.1 m3, P2 = 3 bar. Pressure and volume are related linearly during the process. For the gas, find the work, in kJ. Solution The pressure – volume relation in this case is linear. For this process, V1 = 0.3 m3, P1 = 1 bar to V2 = 0.1 m3, P2 = 3 bar Thus, using the equation of a straight line, we have: 𝑃2 − 𝑃1 𝑃 − 𝑃1 = 𝑉2 − 𝑉1 𝑉 − 𝑉1 Or 3−1 𝑃−1 = 0.1 − 0.3 𝑉 − 0.3  Which gives 𝑃 = 4 − 10𝑉, bar With P in bar. For pressure in N/m2, simply multiply by 105 so that: 𝑃 = (4 − 10𝑉) × 105 N/m2 Work done on the system is given by: 𝑉2 𝑊 = ∫ 𝑃 𝑑𝑉 𝑉1 or 0.1 𝑊 = 105 ∫ (4 − 10𝑉) 𝑑𝑉 = −𝟒𝟎 𝒌𝑱 0.3 This is basic integration.…. 3. A gas expands from an initial state where P1 = 500 kPa and V1 = 0.1 m3 to a final state where P2 = 100 kPa. The relationship between pressure and volume during the process is PV = constant. Sketch the process on a p–V diagram and determine the work, in kJ. Solution For this process, P1 = 500 kPa (or 5 × 105 𝑁/𝑚2 ), V1 = 0.1 m3, P2 = 100 kPa (or 1 × 105 𝑁/𝑚2 Since PV = constant, we can say that P1V1= P2V2 P1 V1 500×0.1 Or V2 = = = 𝟎. 𝟓 𝒎𝟑 P2 100 Work done by the system is given by: 𝑉2 𝑉2 𝑑𝑉 𝑊 = ∫ 𝑃 𝑑𝑉 = 𝐶 ∫ 𝑉 𝑉1 𝑉1 𝑽 Where C is a constant. Integrating gives 𝑾 = 𝑷𝟏 𝑽𝟏 𝐥𝐧 (𝑽𝟐 ) 𝟏 Since 𝑃1 𝑉1 = 𝑃2 𝑉2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Therefore, 𝑉2 𝑁 0.5 𝑊 = 𝑃1 𝑉1 ln ( ) = (5 × 105 2 ) × (0.1 𝑚2 ) × ln ( ) 𝑉1 𝑚 0.1 Or 𝑊 = +80,472 𝐽 ≈ +𝟖𝟎. 𝟒𝟕 𝒌𝑱 Now, try these on your own… 1. Warm air is enclosed in a horizontal piston–cylinder assembly shown in the figure below: Initially, the air has a volume of 0.003 m³, and the volume decreases to 0.002 m³ during the process. A spring exerts a linearly decreasing force on the piston, starting from 900 N at the beginning of the process and reducing to zero by the end. Atmospheric pressure is 100 kPa, and the piston face has an area of 0.018 m². Neglecting friction between the piston and cylinder wall: a. Determine the initial and final pressures of the air (in kPa). b. Calculate the work done during the process (in kJ). 2. Air undergoes a two-step thermodynamic process:  Process 1–2: A polytropic compression with n=1.3, starting at an initial pressure p1=100 kPa and specific volume v1=0.04 m3/kg, and ending at a specific volume v2=0.02 m3/kg.  Process 2–3: A constant-pressure expansion from v2 to v3=v1. (a) Sketch the processes on a p – v diagram. (b) Determine the work done per unit mass of air for the entire process, in kJ/kg. 3. A certain gas obeys the molar equation of state P(V-b) = RT, where R is the universal gas constant, and b is a constant such that 0