The document discusses the second law of thermodynamics and Carnot cycle. It defines the second law and provides statements by Clausius, Kelvin, and Planck. It then discusses heat engines, defining them as devices that continuously convert heat to work in a cyclic process using a working fluid. The document also covers:
- The Carnot cycle, which uses reversible processes between two heat reservoirs
- The four processes of the Carnot cycle: two isothermal and two adiabatic processes
- Equations to calculate efficiency, work, heat transfer, and entropy for the Carnot cycle
- Two sample problems are provided to demonstrate calculating values for a Carnot cycle operating between given temperature limits.
The document discusses the second law of thermodynamics and Carnot cycle. It defines the second law and provides statements by Clausius, Kelvin, and Planck. It then discusses heat engines, defining them as devices that continuously convert heat to work in a cyclic process using a working fluid. The document also covers:
- The Carnot cycle, which uses reversible processes between two heat reservoirs
- The four processes of the Carnot cycle: two isothermal and two adiabatic processes
- Equations to calculate efficiency, work, heat transfer, and entropy for the Carnot cycle
- Two sample problems are provided to demonstrate calculating values for a Carnot cycle operating between given temperature limits.
The document discusses the second law of thermodynamics and Carnot cycle. It defines the second law and provides statements by Clausius, Kelvin, and Planck. It then discusses heat engines, defining them as devices that continuously convert heat to work in a cyclic process using a working fluid. The document also covers:
- The Carnot cycle, which uses reversible processes between two heat reservoirs
- The four processes of the Carnot cycle: two isothermal and two adiabatic processes
- Equations to calculate efficiency, work, heat transfer, and entropy for the Carnot cycle
- Two sample problems are provided to demonstrate calculating values for a Carnot cycle operating between given temperature limits.
The document discusses the second law of thermodynamics and Carnot cycle. It defines the second law and provides statements by Clausius, Kelvin, and Planck. It then discusses heat engines, defining them as devices that continuously convert heat to work in a cyclic process using a working fluid. The document also covers:
- The Carnot cycle, which uses reversible processes between two heat reservoirs
- The four processes of the Carnot cycle: two isothermal and two adiabatic processes
- Equations to calculate efficiency, work, heat transfer, and entropy for the Carnot cycle
- Two sample problems are provided to demonstrate calculating values for a Carnot cycle operating between given temperature limits.
Heat engine Application of Ideal Gas Processes 2nd Law of Thermodynamics 2nd Law of Thermodynamics The second law of thermodynamics has been enunciated meticulously by Clausius, Kelvin and Planck in slightly different words although both statements are basically identical. Each statement is based on an irreversible process. The first considers transformation of heat between two thermal reservoirs while the second considers the transformation of heat into work 2nd Law of Thermodynamics “It is impossible for a self-acting machine working in a cyclic process unaided by any external agency, to convey heat from a body at a lower temperature to a body at a higher temperature”. – Clausius “It is impossible to construct an engine, which while operating in a cycle produces no other effect except to extract heat from a single reservoir and do equivalent amount of work”. – Kelvin and Planck The second law of thermodynamics may be written in several ways. Regardless of the terminology used, however, the purpose of the second law is to give the sense of direction to energy-transfer. The second law of thermodynamics states: “Whenever energy is transferred, the value of energy cannot be conserved, and some energy must be permanently reduced to a lower value.” 2nd Law of Thermodynamics When this is combined with the first law of thermodynamics, the law of energy conservation, the following results:
“Whenever energy is transferred, energy must be conserved, but the
value of energy cannot be conserved, and some energy must be permanently reduced to a lower value.” Heat Engines & Thermal Engine Heat engine is a device that continuously converts heat to work (or power). The word ‘continuous’ is of critical importance in this definition and needs further elaboration; it means that the engine will continue to operate if the heat energy input is maintained. The ability of the device to convert heat to work does not necessarily make the device a heat engine. A heat engine is a device that operates in a cycle. Heat Engines & Thermal Engine 1. Heat engines differ considerably from one another, but all can be characterized by the following: 2. They receive heat from a high-temperature source (solar energy, oil furnace, nuclear reactor, etc.). 3. They convert part of this heat to work (usually in the form of a rotating shaft). 4. They reject the remaining waste heat to a low-temperature sink (the atmosphere, rivers, etc.). 5. They operate on a cycle. 6. Heat engines and other cyclic devices usually involve a fluid to and from which heat is transferred while undergoing a cycle. This fluid is called the working fluid. Corollary of 2nd Law of Thermodynamics First Corollary of the Second Law The second law gives a sense of direction to a process, whereas the first law does not. It also tells us that it is impossible to have perpetual-motion machine of the second kind, one that violates the second law. The first of two corollaries to this law states: “It is impossible to construct an engine to operate between two heat reservoirs, each having a fixed and uniform temperature, that will exceed the efficiency of reversible engine operating between the same reservoirs.” Corollary of 2nd Law of Thermodynamics The second corollary of the second law states: “All reversible engines have the same efficiency when working between the same two constant temperature heat reservoirs.”
Work of a Cycle If there is no change in stored energy during cyclic
operation of a system, which may be steady or non-flow, the net amount of energy crossing the boundary as heat equal to the net amount of energy crossing the boundary as work. Corollary of 2nd Law of Thermodynamics • 𝑊𝑛𝑒𝑡 = 𝛴𝑊 = ΣQ 𝑊𝑛𝑒𝑡 = ∫ 𝑃𝑑𝑣
• Reversible Non – Flow Process
𝑊𝑛𝑒𝑡 = −∫ 𝑉𝑑𝑝
• Reversible Steady – Flow Process
𝑊𝑛𝑒𝑡 = ∫ 𝑇 𝑑𝑆 Corollary of 2nd Law of Thermodynamics • Thermal Efficiency The thermal 𝑊𝑛𝑒𝑡 efficiency may well be thought 𝑒𝑐𝑦𝑐𝑙𝑒 = 𝑄𝐴 of in its simplest form, output divided by input. • The output of a power cycle is 𝑊𝑛𝑒𝑡 = 𝑄𝐴 − 𝑄𝑅 the network and the input are the heat added to the working substance from an external source of heat Carnot Cycle The cycle was first suggested by a French engineer Sadi Carnot in 1824 which works on reversible cycle and is known as Carnot cycle. Any fluid may be used to operate the Carnot cycle which is performed in an engine cylinder the head of which is supposed alternatively to be perfect conductor or a perfect insulator of a heat. Heat is caused to flow into the cylinder by the application of high temperature energy source to the cylinder head during expansion, and to flow from the cylinder by the application of a lower temperature energy source to the head during compression. Carnot Cycle Carnot Cycle • The assumptions made for describing the working of the Carnot engine are as follows: • The piston moving in a cylinder does not develop any friction during motion. • The walls of piston and cylinder are considered as perfect insulators of heat. • The cylinder head is so arranged that it can be a perfect heat conductor or perfect heat insulator. • The transfer of heat does not affect the temperature of source or sink. • Working medium is a perfect gas and has constant specific heat. • Compression and expansion are reversible. Carnot Cycle Processes • Process 1 – 2: Isothermal Expansion • Hot energy source is applied. Heat Q1 is taken in whilst the fluid expands isothermally and reversibly at constant high temperature T1. • Process 2 – 3: Isentropic Expansion • The cylinder becomes a perfect insulator so that no heat flow takes place. The fluid expands adiabatically and reversibly whilst temperature falls from T1 to T2. Carnot Cycle Processes • Process 3 – 4: Isothermal Compression • Cold energy source is applied. Heat Q2 flows from the fluid whilst it is compressed isothermally and reversibly at constant lower temperature T2. • Process 4 – 1: Isentropic Compression • Cylinder head becomes a perfect insulator so that no heat flow occurs. The compression is continued adiabatically and reversibly during which temperature is raised from T2 to T1. Carnot Cycle Processes • The work delivered from the system during the cycle is represented by the enclosed area of the cycle. Again, for a closed cycle, according to first law of the thermodynamics the work obtained is equal to the difference between the heat supplied by the source (Q1) and the heat rejected to the sink (Q2). Analysis of Carnot Cycle 𝑉2 𝑄𝐴 = 𝑇1 𝑆2 − 𝑆1 = 𝑚𝑅𝑇1 𝑙𝑛 𝑉1 𝑉4 𝑄𝑅 = 𝑇3 (𝑆4 − 𝑆3 ) = 𝑚𝑅𝑇3 𝑙𝑛 𝑉3
𝑊 = 𝑄𝐴 − 𝑄𝑅 = (𝑇1 −𝑇3 )(𝑆2 − 𝑆1 )
𝑊 𝑒= ; efficiency 𝑄𝐴 𝑊 𝑃𝑚 = ; mean effective Pressure 𝑉𝐷 Problem 1 A Carnot cycle receives 1000 BTU of heat while operating between temperature limits of 1000°R and 500°R. Determine the cycle efficiency, heat rejected, work of the cycle and the entropy change during heat addition. Problem 2 Gaseous nitrogen actuates a Carnot power cycle in which the respective volumes at the four corners of the cycle, starting at the beginning of the isothermal expansion, are V1 = 0.3565 ft3, V2 = 0.5130 𝑓𝑡 3 , V3 = 8.0 𝑓𝑡 3 , and V4 = 5.57 𝑓𝑡 3 . What is the thermal efficiency?
“Foundations to Flight: Mastering Physics from Curiosity to Confidence: Cipher 4”: “Foundations to Flight: Mastering Physics from Curiosity to Confidence, #4