Zeroth, First, and Second Laws of Thermodynamics

Michael Kurniawan 1910403011 University of Cincinnati ZEROTH, FIRST, AND SECOND LAWS OF THERMODYNAMICS 1. If system A is in thermal equilibrium with system B, and system B is in thermal equilibrium with system C, are systems A and C in thermal equilibrium? Explain. Yes, systems A and C are in thermal equilibrium. This is the essence of the Zeroth Law of Thermodynamics. It states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This implies that all three systems have the same temperature, allowing us to use a thermometer to measure temperature consistently. 2. Two objects, one with a temperature of 300 K and the other with a temperature of 400 K, are placed in thermal contact. What will happen according to the zeroth law of thermodynamics? According to the Zeroth Law of Thermodynamics, if two objects are placed in thermal contact, heat will flow from the object at a higher temperature (400 K) to the object at a lower temperature (300 K) until thermal equilibrium is reached. At equilibrium, both objects will have the same temperature. The Zeroth Law underlies the principle that heat transfer will occur until a common temperature is achieved, but it does not directly describe the heat transfer process itself. 3. A thermometer is used to measure the temperature of two objects. If the thermometer shows the same temperature for both objects, what can be said about the thermal state of these two objects? If the thermometer shows the same temperature for both objects, it can be said that the two objects are in thermal equilibrium with each other. According to the Zeroth Law of Thermodynamics, if two systems are each in thermal equilibrium with a third system (the thermometer), then they are in thermal equilibrium with each other. This means there is no net flow of heat between the two objects, and they have the same temperature. 4. An ideal gas undergoes a process where 150 J of heat is added to the system and 50 J of work is done by the system. What is the change in the internal energy of the system? The First Law of Thermodynamics states that the change in the internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system: The change in the internal energy of the system is 100 J. 5. In a thermodynamic cycle, a heat engine receives 500 J of heat from a hot reservoir and expels 300 J of heat to a cold reservoir. Calculate the work done by the engine. In a thermodynamic cycle, the work done (W) by the engine is the difference between the heat absorbed from the hot reservoir (QH) and the heat expelled to the cold reservoir (QC): The work done by the engine is 200 J. 6. A piston containing gas undergoes an isobaric (constant pressure) expansion where 200 J of work is done by the gas. If 500 J of heat is added to the system, what is the change in the internal energy of the gas? 7. A Carnot engine operates between a hot reservoir at a temperature of 600 K and a cold reservoir at a temperature of 300 K. Calculate the maximum efficiency of the engine. 8. A refrigerator operates by expelling 200 J of heat to the environment and taking in 100 J of heat from inside the refrigerator. Calculate the coefficient of performance (COP) of the refrigerator. 9. A heat engine receives 1000 J of heat from a hot reservoir and does 400 J of work. Calculate the entropy generated in this process if the hot reservoir is at 500 K and the cold reservoir is at 300 K. The total entropy change (ΔStotal ) is the sum of the changes in entropy of the hot and cold reservoirs: 10. Explain why it is impossible to create an engine with 100% efficiency based on the Second Law of Thermodynamics. The Second Law of Thermodynamics states that no heat engine can be 100% efficient because some energy will always be lost as waste heat to the surroundings. This is due to the fact that in any thermodynamic cycle, there must be a heat flow from the hot reservoir to the cold reservoir. According to the law, entropy of an isolated system always increases in a real, spontaneous process. Mathematically, the efficiency of a heat engine is given by: where QC is the heat expelled to the cold reservoir and QH is the heat absorbed from the hot reservoir. For an engine to be 100% efficient (η=1), QC would have to be zero, meaning no heat is expelled to the cold reservoir. This violates the Second Law of Thermodynamics because it would imply a decrease in entropy, which is not possible. Therefore, it is impossible to create an engine that converts all the absorbed heat into work without expelling some heat to a colder reservoir, making 100% efficiency unattainable.