Thermodynamic Processes And Cycles

Michael Kurniawan 1910403011 University of Cincinnati THERMODYNAMIC PROCESSES AND CYCLES 1. A gas undergoes an adiabatic expansion, and its initial temperature is 400 K. If the initial pressure is 2 atm and the final pressure is 1 atm, calculate the final temperature. (Assume γ=1.4 for the gas). For an adiabatic process, the relationship between temperature and pressure is given by: 2. A gas is compressed adiabatically, and its temperature increases from 300 K to 600 K. If the initial pressure is 1 atm, calculate the final pressure. (Assume γ=1.4 for the gas) The final pressure is 8 atm. 3. In an isobaric process, 500 J of heat is added to a gas, and the gas expands. Calculate the work done by the gas and the change in internal energy of the gas. For an isobaric process (constant pressure), the work done by the gas is given by: The First Law of Thermodynamics states: Since we need to find both the work done and the change in internal energy, we assume that all the heat added goes into doing work and changing internal energy. Therefore, the work done by the gas is 500 J, and the change in internal energy is 0 J. 4. A gas undergoes an isochoric heating process where its temperature increases from 200 K to 400 K. If the heat added is 1000 J, calculate the change in internal energy of the gas. For an isochoric process (constant volume), no work is done, so the heat added to the system is equal to the change in internal energy: The change in internal energy is 1000 J. 5. In an isothermal compression, a gas does 200 J of work on the surroundings. Calculate the amount of heat exchanged with the surroundings. For an isothermal process (constant temperature), the change in internal energy (ΔU) is zero. According to the First Law of Thermodynamics: The amount of heat exchanged with the surroundings is 200 J 6. Describe the four processes in a Carnot cycle and explain why it is considered the most efficient cycle. The Carnot cycle consists of four reversible processes: 1. Isothermal Expansion (A to B): The gas expands isothermally at the temperature TH, absorbing heat QH from the hot reservoir. During this process, the system does work on the surroundings. 2. Adiabatic Expansion (B to C): The gas continues to expand without any heat exchange (adiabatically), and its temperature decreases from TH to TC. 3. Isothermal Compression (C to D): The gas is compressed isothermally at the temperature TC, expelling heat QC to the cold reservoir. During this process, work is done on the system by the surroundings. 4. Adiabatic Compression (D to A): The gas is compressed adiabatically, causing its temperature to rise from TC back to TH, completing the cycle. Efficiency Explanation: The Carnot cycle is considered the most efficient because it is a reversible cycle operating between two heat reservoirs. The efficiency of a Carnot engine is given by: This efficiency depends only on the temperatures of the hot and cold reservoirs and is the maximum possible efficiency for any heat engine operating between these two temperatures. No real engine can exceed the Carnot efficiency because real processes involve irreversibilities and non-idealities that the Carnot cycle avoids. 7. In an Otto cycle, the compression ratio is 8:1, and the initial temperature before compression is 300 K. Calculate the temperature after adiabatic compression. (Assume γ=1.4). For adiabatic compression in an Otto cycle, the relationship between temperatures and volumes is given by: The temperature after adiabatic compression is approximately 791.7 K. 8. A refrigerator operates on a reverse Carnot cycle between temperatures of 250 K and 300 K. Calculate the coefficient of performance (COP) of the refrigerator. The coefficient of performance (COP) of a refrigerator operating on a reverse Carnot cycle is given by: The coefficient of performance of the refrigerator is 5. 9. A heat engine operates on a Rankine cycle. If the heat added in the boiler is 2000 J and the work done by the turbine is 500 J, calculate the efficiency of the cycle. The efficiency (η\etaη) of a Rankine cycle is given by: The efficiency of the Rankine cycle is 25%. 10. Explain the differences between the Brayton cycle and the Rankine cycle, and identify which one is typically used in jet engines and why. Brayton Cycle: • The Brayton cycle is a thermodynamic cycle that describes the workings of a constant-pressure heat engine. • It consists of four processes: isentropic compression, isobaric (constant pressure) heat addition, isentropic expansion, and isobaric heat rejection. • It is typically used in gas turbines and jet engines. • The working fluid remains in the gas phase throughout the entire cycle. Rankine Cycle: • The Rankine cycle is a thermodynamic cycle used to convert heat into work, often employed in steam power plants. • It consists of four processes: isentropic compression (pump), isobaric heat addition (boiler), isentropic expansion (turbine), and isobaric heat rejection (condenser). • It typically involves a phase change from liquid to vapor and back to liquid. • The working fluid undergoes phase changes, making it suitable for steam engines and power plants. Jet Engines: • The Brayton cycle is typically used in jet engines because it operates with a high flow rate of air and fuel, and the working fluid remains in the gas phase, which is ideal for the continuous combustion process needed in jet propulsion. • Jet engines rely on the principles of the Brayton cycle to compress incoming air, mix it with fuel, ignite the mixture to produce hightemperature, high-pressure gases, and then expand these gases through a turbine and exhaust nozzle to produce thrust.