Thermodynamics: how 9 AI study apps did on 20 college problems

A regenerative gas-turbine cycle uses air as the working fluid. The compressor pressure ratio is 8.5. Air enters the compressor at 295 K and the turbine at 1260 K. The compressor has an isentropic efficiency of 80 percent, the turbine 86 percent, and the regenerator effectiveness is 70 percent. Neglect pressure losses. Accounting for the variation of specific heats with temperature (use the ideal-gas properties of air, Çengel Table A-17), determine: (a) the air temperature at the turbine exit, in K; (b) the net work output, in kJ/kg; (c) the thermal efficiency; (d) the back work ratio.

A gas-turbine plant delivers a net shaft output of 7200 kW. Air is compressed in two stages with equal pressure ratios and complete intercooling; the overall pressure ratio is 10 and air enters each compressor stage at 25°C. A high-pressure turbine drives the two compressors and nothing else; a separate low-pressure (power) turbine drives the load. Gas enters the high-pressure turbine at 680°C and is reheated to 680°C before entering the low-pressure turbine. The low-pressure turbine exhaust passes through a heat exchanger that heats the air leaving the second compressor stage; its thermal ratio, defined as (air temperature rise)/(gas inlet temperature − air inlet temperature), is 0.75. The isentropic efficiency of each compressor stage is 0.82 and of each turbine is 0.87. Both shafts have a mechanical efficiency of 96 percent: 0.96 × (high-pressure turbine work) = total compressor work, and net output = 0.96 × (low-pressure turbine work). Neglect pressure losses, kinetic energy changes and the mass of fuel. For air take cp = 1.005 kJ/kg·K and γ = 1.4; for the gases in the combustion chamber, reheater, turbines and heat exchanger take cp = 1.147 kJ/kg·K and γ = 1.333 (use these gas values for the heat supplied in the combustion chamber and in the reheater). Determine: (a) the thermal efficiency of the plant (net output / total heat supplied); (b) the work ratio (net output / total gross turbine work); (c) the mass flow rate of air, in kg/s.

A steam power plant operates on a reheat–regenerative Rankine cycle with one open feedwater heater and has a net power output of 120 MW. Steam enters the high-pressure turbine at 12 MPa and 560°C and expands to 1 MPa. At 1 MPa some steam is extracted to the open feedwater heater; the rest is reheated at 1 MPa to 480°C and expands in the low-pressure turbine to the condenser pressure of 8 kPa. Water leaves the condenser and the feedwater heater as saturated liquid. Both turbines have an isentropic efficiency of 87 percent and both pumps 85 percent. Neglect pressure drops and kinetic energy changes. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the fraction of the boiler steam that is extracted; (b) the mass flow rate of steam through the boiler, in kg/s; (c) the thermal efficiency of the cycle; (d) the quality of the steam at the low-pressure turbine exit.

A steam turbine plant produces 150 MW of net electrical output. It has reheating and two feed heaters: a closed (surface) heater on the high-pressure side and an open (direct-contact) heater on the low-pressure side. Steam at the stop valve is at 120 bar and 540°C and is throttled to 114 bar before entering the high-pressure turbine, which exhausts at 28 bar. Part of this exhaust is bled to the closed heater; the rest is reheated to 560°C and enters the low-pressure turbine at 25 bar (the reheater pressure drop is 3 bar). Steam is bled from the low-pressure turbine at 7 bar to the open heater, and the rest expands to 0.06 bar. Treat the low-pressure turbine as two sections (25 → 7 bar and 7 → 0.06 bar), each with the turbine isentropic efficiency. The condensate pump raises the condenser water (saturated liquid at 0.06 bar) to 7 bar. The open heater delivers saturated liquid at 7 bar to the boiler feed pump, which raises it to 120 bar; the feedwater then passes through the closed heater, leaving it at the saturation temperature of the bled steam (28 bar), and enters the boiler. The drain from the closed heater leaves as saturated liquid at 28 bar and is throttled into the open heater. Neglect the boiler pressure drop. Turbine isentropic efficiency (each section) 86 percent; pump isentropic efficiency 88 percent; mechanical efficiency 96 percent; generator efficiency 97 percent; boiler efficiency 91 percent. Net electrical output = 0.96 × 0.97 × (total turbine work) − (total pump work). Overall efficiency = net electrical output / fuel energy, where fuel energy = (heat to steam in the boiler + heat in the reheater)/0.91. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the steam bled to the closed heater, in kg/h; (b) the steam bled to the open heater, in kg/h; (c) the overall thermal efficiency of the plant; (d) the specific steam consumption (boiler steam per kWh of net electrical output), in kg/kWh.

The gas-turbine cycle of a combined gas–steam power plant has a pressure ratio of 14. Air enters the compressor at 300 K and the turbine at 1450 K. The compressor isentropic efficiency is 86 percent and the gas-turbine isentropic efficiency is 89 percent. The gases leaving the gas turbine heat steam at 14 MPa to 520°C in a heat-recovery steam generator and leave it at 230°C. The steam expands isentropically in a high-pressure turbine to 3 MPa, is reheated at 3 MPa to 560°C in the combustion chamber, and expands isentropically in a low-pressure turbine to 8 kPa. It is condensed to saturated liquid and pumped isentropically to 14 MPa. The steam flow rate is 15 kg/s. Treat the combustion gases as air with variable specific heats (Çengel Table A-17), neglect the mass of fuel, and use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the mass flow rate of air, in kg/s; (b) the total rate of heat input in the combustion chamber (including the steam reheat), in kW; (c) the net power output of the combined plant, in MW; (d) the thermal efficiency of the combined cycle.

A binary vapour cycle uses mercury and steam. Dry saturated mercury vapour at 4.5 bar enters the mercury turbine and exhausts at 0.04 bar. Mercury leaves the mercury condenser as saturated liquid at 0.04 bar and is pumped back to 4.5 bar. The mercury condenser is the steam boiler: it turns feedwater into dry saturated steam at 18 bar. This steam is then superheated to 320°C in a superheater placed in the mercury-boiler furnace and expands in a steam turbine to 0.05 bar; the condensate (saturated liquid at 0.05 bar) is pumped to 18 bar. The mercury turbine has an internal (isentropic) efficiency of 0.85 and the steam turbine 0.87; both pumps are isentropic and their work must be included. The steam flow is 52 000 kg/h. Properties of saturated mercury: | p (bar) | t (°C) | hf (kJ/kg) | hg (kJ/kg) | sf (kJ/kg·K) | sg (kJ/kg·K) | vf (m³/kg) | vg (m³/kg) | |---|---|---|---|---|---|---|---| | 4.5 | 450 | 62.93 | 355.98 | 0.1352 | 0.5397 | 79.9 × 10⁻⁶ | 0.068 | | 0.04 | 216.9 | 29.98 | 329.85 | 0.0808 | 0.6925 | 76.5 × 10⁻⁶ | 5.178 | Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7) for water. Determine: (a) the mercury flow rate, in kg/h; (b) the overall efficiency of the binary cycle (net work of both cycles / heat supplied in the mercury boiler and the superheater); (c) the net power output, in MW.

An insulated vertical piston–cylinder device initially contains 12 kg of water, 9 kg of which is vapour. The piston maintains a constant pressure of 400 kPa. Steam from a supply line at 3 MPa and 450°C is admitted until all the liquid in the cylinder has just vaporized. The surroundings are at 25°C and 100 kPa. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the mass of steam that entered, in kg; (b) the final volume of the cylinder, in m³; (c) the boundary work done by the steam, in kJ; (d) the exergy destroyed during the process, in kJ.

Steam expands adiabatically in a turbine from 2.8 MPa and 430°C to 450 kPa and 235°C at a rate of 6.5 kg/s. The dead state is 25°C and 100 kPa. Neglect kinetic and potential energy changes. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the isentropic efficiency of the turbine; (b) the reversible (maximum) work per kg of steam, in kJ/kg; (c) the rate of irreversibility (exergy destruction), in kW; (d) the second-law efficiency of the turbine.

Two rigid tanks are connected by a valve. Tank A is insulated and contains 0.25 m³ of steam at 500 kPa with a quality of 70 percent. Tank B is uninsulated and contains 3 kg of steam at 250 kPa and 280°C. The valve is opened and steam flows from tank A to tank B until the pressure in tank A has dropped to 250 kPa; the valve is then closed. During the process 250 kJ of heat is transferred from tank B to the surroundings at 20°C. Assume the steam remaining in tank A undergoes a reversible adiabatic process. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the final temperature in tank A, in °C; (b) the final temperature in tank B, in °C; (c) the final pressure in tank B, in kPa; (d) the total entropy generated during the process, in kJ/K.

Steam initially at 1.8 MPa with a dryness fraction of 0.96 expands isentropically to 800 kPa and is then throttled until it is just dry saturated. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Per kg of steam, determine: (a) the dryness fraction at the end of the isentropic expansion; (b) the pressure at the end of throttling, in kPa; (c) the total change in entropy, in kJ/kg·K; (d) the total change in enthalpy, in kJ/kg; (e) the total change in internal energy, in kJ/kg.

A vertical piston–cylinder device initially contains 0.02 m³ of steam at 600 kPa and 220°C. The frictionless piston maintains a constant pressure of 600 kPa. Steam from a supply line at 1.4 MPa and 380°C is admitted until the volume inside the cylinder triples. Neglect any heat transfer. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the final temperature of the steam in the cylinder, in °C; (b) the mass of steam that entered, in kg; (c) the boundary work done, in kJ.

A piston–cylinder device contains 2.5 kg of wet steam at 900 kPa with a dryness fraction of 0.97. The steam expands reversibly according to pv^1.08 = constant to 40 kPa. The piston is then locked and the steam is cooled at constant volume until its pressure is 20 kPa. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the work done during the expansion, in kJ; (b) the heat transfer during the expansion, in kJ (positive if heat is added); (c) the dryness fraction at the end of the expansion; (d) the heat transfer during the constant-volume cooling, in kJ (negative if heat is removed); (e) the dryness fraction at the end of the cooling.

Air at a total pressure of 85 kPa, 34°C and 65 percent relative humidity enters a 35-cm-diameter cooling section at a velocity of 150 m/min. It is cooled by a coil through which chilled water flows; the water temperature rises by 7°C. The air leaves the cooling section saturated at 18°C, and the condensate leaves at 18°C. Take cp of water = 4.18 kJ/kg·K. Because the pressure is not 1 atm, do not use a standard psychrometric chart: use the ideal-gas relations with saturation pressures from steam tables, h = 1.005T + ω(2500.9 + 1.82T) kJ/kg dry air (T in °C) and R_air = 0.287 kJ/kg·K. Determine: (a) the rate of heat removal from the air, in kJ/min; (b) the mass flow rate of the chilled water, in kg/min; (c) the exit velocity of the air, in m/min; (d) the rate of condensate removal, in kg/min.

A cooling tower cools 7.2 kg/s of water that enters at 42°C. A fan draws 11 m³/s of atmospheric air (volume measured at the inlet state) through the tower and absorbs 5.5 kW, all of which ends up in the streams. The air enters at 20°C and 55 percent relative humidity and leaves saturated at 28°C. The total pressure is 100.5 kPa throughout. Use the ideal-gas relations with saturation pressures from steam tables, h = 1.005T + ω(2500.9 + 1.82T) kJ/kg dry air (T in °C), R_air = 0.287 kJ/kg·K, and take the water enthalpies as saturated-liquid values at their temperatures. Determine: (a) the mass flow rate of dry air, in kg/s; (b) the make-up water required, in kg/s; (c) the temperature of the water leaving the tower, in °C.

An insulated tank containing 1.5 kg of CO₂ at 30°C and 250 kPa is connected by a valve to an uninsulated 3-m³ tank containing N₂ at 60°C and 450 kPa. The valve is opened and the two gases form a homogeneous mixture that comes to 20°C, the temperature of the surroundings. Treat both gases as ideal gases with constant specific heats at room temperature from Çengel Table A-2a (CO₂: R = 0.1889, cp = 0.846, cv = 0.657; N₂: R = 0.2968, cp = 1.039, cv = 0.743, all kJ/kg·K; molar masses 44.01 and 28.01 kg/kmol). Determine: (a) the final pressure, in kPa; (b) the heat transferred to the surroundings, in kJ; (c) the entropy generated, including the surroundings, in kJ/K; (d) the exergy destroyed, in kJ (T₀ = 20°C).

An insulated rigid tank of 1.8 m³ contains superheated steam at 4.5 MPa and 480°C. A valve is opened and steam flows out of the tank through an adiabatic turbine that exhausts to a line at 100 kPa. The turbine has an isentropic efficiency of 80 percent at every instant. The valve is closed when the tank pressure has fallen to 600 kPa. Assume the steam that remains in the tank undergoes a reversible adiabatic process, and neglect kinetic and potential energies. Use steam tables (IAPWS-95, e.g. Çengel Tables A-4 to A-7). Determine: (a) the mass of steam that left the tank, in kg; (b) the final temperature of the steam in the tank, in °C; (c) the total work produced by the turbine, in kJ; (d) the total entropy generated during the process, in kJ/K.

Methane (CH₄) at 25°C is burned at a constant pressure of 1 atm in an adiabatic combustor with 10 percent excess oxygen supplied as oxygen-enriched air of composition 30 percent O₂ and 70 percent N₂ by mole, also at 25°C. The products leave as an equilibrium mixture of CO₂, CO, H₂O, H₂, O₂ and N₂ only (the reactions to consider are CO₂ ⇌ CO + ½O₂ and H₂O ⇌ H₂ + ½O₂; neglect OH, O, H, NO and N₂ dissociation). Use ideal-gas enthalpies (Çengel Tables A-18 to A-26 or the equivalent JANAF data) and equilibrium constants from Çengel Table A-28. Determine: (a) the adiabatic flame temperature, in K; (b) the mole fraction of CO in the products (wet basis, water vapour included), in percent; (c) the mole fraction of H₂ in the products (wet basis), in percent; (d) the adiabatic flame temperature that complete combustion (no dissociation) would give, in K.

A two-stage compression refrigeration system uses refrigerant-134a and operates between 1.2 MPa and 0.12 MPa. The refrigerant leaves the condenser as saturated liquid and is throttled to a flash chamber at 0.4 MPa. The vapour formed in the flash chamber is mixed with the refrigerant leaving the low-pressure compressor, and the mixture is compressed to 1.2 MPa by the high-pressure compressor. The saturated liquid from the flash chamber is throttled to 0.12 MPa and leaves the evaporator as saturated vapour. Both compressors have an isentropic efficiency of 82 percent. The system removes 30 kW from a refrigerated space kept at −15°C and rejects heat to surroundings at 25°C. Use R-134a tables (Çengel Tables A-11 to A-13). Determine: (a) the fraction of the refrigerant that vaporizes in the flash chamber; (b) the mass flow rate of refrigerant through the condenser, in kg/s; (c) the total compressor power, in kW; (d) the coefficient of performance; (e) the total rate of exergy destruction, in kW, taking the system boundary at the temperatures of the refrigerated space (−15°C) and the surroundings (25°C), so that the irreversibilities of the heat transfers to and from the refrigerant are included.

At a high-altitude site the atmospheric pressure is 84 kPa. A sling psychrometer reads a dry-bulb temperature of 38°C and a wet-bulb temperature of 21°C; take the wet-bulb temperature as equal to the adiabatic saturation temperature. Do not use a psychrometric chart (it is drawn for 101.325 kPa). Determine: (a) the humidity ratio of the air, in kg water/kg dry air; (b) the relative humidity, in percent; (c) the dew-point temperature, in °C. This air then passes through an adiabatic evaporative cooler and leaves at 80 percent relative humidity (neglect the enthalpy of the water added). Determine: (d) the temperature of the air leaving the cooler, in °C; (e) the water added, in kg per kg of dry air.

Air flows through a converging–diverging nozzle from a large reservoir at 900 kPa and 650 K. The throat area is 30 cm² and the exit area is 75 cm². The back pressure is 600 kPa, and a normal shock stands in the diverging section. Assume one-dimensional isentropic flow everywhere except across the shock, and treat air as an ideal gas with k = 1.4, R = 0.287 kJ/kg·K and cp = 1.005 kJ/kg·K. Determine: (a) the mass flow rate, in kg/s; (b) the cross-sectional area at the location of the shock, in cm²; (c) the Mach number just upstream of the shock; (d) the Mach number at the nozzle exit; (e) the entropy generated per unit mass of air, in kJ/kg·K.