Introduction to 2nd Law of Thermodynamics - Review Sheet for Exam | ME 2233, Study notes of Mechanical Engineering

Download Introduction to 2nd Law of Thermodynamics - Review Sheet for Exam | ME 2233 and more Study notes Mechanical Engineering in PDF only on Docsity! Review: Fundamentals: Conservation of Mass, Conservation of Energy Applications: Nozzles/Diffusers, Throttling, Compressors/Turbines, Heat Exchangers/Mixers Today: Applications with multiple devices. Examples: Text 4.105, 4.104, 4.103 4.105 Separate streams of steam and air flow through the turbine and heat exchanger arrangement shown in Fig. P4.105. Steady-state operating data are provided on the figure. Heat transfer with the surroundings can be neglected, as can all kinetic and potential energy effects. Determine (a) T3 in K, and (b) the power output of the second turbine in kW. 4.104 A residential air conditioning system operates at steady state, as shown in Fig. P4.104. Refrigerant 22 circulates through the components of the system. Property data at key locations are given on the figure. If the evaporator removes energy by heat transfer from the room air at a rate of 600 Btu/min, determine (a) the rate of heat transfer between the compressor and the surroundings, in Btu/min, and (b) the coefficient of performance. 4.103 A simple gas turbine power cycle operating at steady state with air as the working substance is shown in Fig. P4.103. The cycle components include an air compressor mounted on the same shaft as the turbine. The air is heated in the high-pressure heat exchanger before entering the turbine. The air exiting the turbine is cooled in the low-pressure heat exchanger before returning to the compressor. Kinetic and potential energy effects are negligible. The compressor and turbine are adiabatic. Using the ideal gas model for air, determine the (a) power required for the compressor, in hp, (b) power output of turbine, in hp, and (c) thermal efficiency of the cycle. 2nd Law of Thermodynamics Introduction The 2nd law of thermodynamics… 1. establishes the possible direction of a process 2. provides a means for measuring the quality of energy 3. establishes theoretical limits on performance 1. Direction / Possibility of a process - hot water will not get hotter in a cool room - a stationary ball will not suddenly roll up a hill Why not? Energy can still be conserved. Why doesn’t mass fall uphill? Consider a mass, which falls and converts potential energy to internal energy stored in the ground. This internal energy exists as an increase in the velocity and vibrations of molecules in the ground. As these molecules hit the mass, a small force is exerted, but this is negligible for a single molecule. For the mass to be thrown back uphill, the vibrations of many billions of molecules would have to hit the mass in the same direction at the same time. This does not occur because the vibrations are not correlated with each other (they are essentially distributed randomly), so the mass being thrown uphill is extremely unlikely. the energy is less organized in the ground than it was as potential energy when the mass was above ground!! The level of disorganization is measured by entropy 2. Quality of Energy (recall energy is conserved) - pressurized gas in a tank is released 1) to the atmosphere or 2) through a turbine - a water fall is 1) allowed to fall freely or 2) is used to power a generator Where does the energy go? How accessible is it? As the level of disorganization (entropy) increases, the energy becomes less accessible and a loss of potential to do work occurs (an inefficiency). 3. Theoretical Performance Limits - What is the most work that can be extracted from steam entering a turbine? - What is the most efficient refrigerator that can be constructed between given temperatures? Maximum efficiency occurs when energy is used to its fullest potential (minimum disorganization) In reality all processes produces a loss of potential work (heat loss, friction, etc.) e.g., Spontaneous Heat Transfer: However, the heat transfer from TH to the engine requires at least a small temperature difference. Recognize that it is possible for a system to become more organized (the energy in the low T source can be driven back to the high T source with a heat pump), but this requires the surroundings to become disorganized in at least the same amount (quantified by the property entropy). Disorganization always occurs when considering the entire universe! High T Source Low T Source High T Source Q Low T Source Heat Engine Work Out High T Source Q Low T Source Now the system has a net work of Wcycle = WI – WR Since the system exchanges heat with only one reservoir the net work cannot be out (Kelvin-Planck statement) WI < WR Thus, W WI R I R< ⇒ <η η The thermal efficiency of an irreversible power cycle is always less than the thermal efficiency of a reversible power cycle when each operates between the same two thermal reservoirs Read proof of corollary 2 in text IS THERE A MAXIMUM η ? Reconsider the Heat Engine: But, how much less than 100 % ???? H L H cycle Q Q Q W −== 1η %1000 <⇒> ηLQ QH QL High Temperature Reservoir at TH Low Temperature Reservoir at TL Heat Engine W= QH -QL Recall: All reversible power cycles operating between the same two thermal reservoirs have the same thermal efficiency and have larger efficiencies than irreversible cycles. Thus, any reversible cycle gives the largest efficiency. This efficiency only depends on the temperatures of the reservoirs that exchange heat with the cycle: Likewise, the efficiency of a refrigeration cycle is maximized by any reversible process and is only a function of the reservoir temperatures. ),(1max HL H L H cycle rev TTf Q Q Q W =−==η ABSOLUTE TEMPERATURE SCALE The absolute temperature scale is defined such that, for a reversible cycle So: ηmax = −1 T T L H The reference point used is the triple state of water: 273.16 K. Note: A reversible efficiency of 100% can never be achieved because a heat reservoir at absolute zero can never quite be reached H L H L T T Q Q = Example: The data listed below are claimed for a power cycle operating between reservoirs at 727 and 127 C. For each case, determine if any principles of thermodynamics would be violated. a) QH = 600 kJ, W = 200 kJ, QC = 400 kJ b) QH = 400 kJ, W = 240 kJ, QC = 160 kJ c) QH = 400 kJ, W = 210 kJ, QC = 180 kJ COP Maximum Maximum C.O.P. (coefficient of performance) for Refrigerators: Maximum C.O.P. for Heat Pumps: LH L inout in cycle in revrefrig TT T QQ Q W Q − = − ==,β LH H inout out cycle out revhp TT T QQ Q W Q − = − ==,γ Examples: A refrigeration cycle operating between two reservoirs receives energy QC from a cold reservoir at TC = 250 K and rejects heat to a hot reservoir at TH = 300 K. For each of the following cases determine whether the cycle operates reversibly, irreversibly, or is impossible: a) QC = 1000 kJ, W = 400 kJ b) QC = 1500 kJ, QH = 1800 kJ c) QH = 1500 kJ, W = 200 kJ d) β = 4 An inventor claims to have developed a device that executes a power cycle while operating between reservoirs at 900 K and 300 K that has a thermal efficiency of (a) 66% and (b) 50%. Evaluate the claim.