Homework Chapter2. Homework Chapter3

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Homework Chapter2 2/1 A storage tank holds methane at 120 K, with a quality of 25 %, and it warms up by 5 C per hour due to a failure in the refrigeration system.

1 Homework Chapter2 2/1 A storage tank holds methane at 120 K, with a quality of 25 %, and it warms up by 5 C per hour due to a failure in the refrigeration system. How long time will it take before the methane becomes single phase and what is the pressure then? 2/2 A 1 m 3 rigid tank has propane at 100 kpa, 300 K and connected by a valve to another tank of 0.5 m 3 with propane at 250 kpa, 400 K. The valve is opened and the two tanks come to a uniform state at 325 K. What is the final pressure? 2/3 Argon is kept in a rigid 5 m 3 tank at 30 C, 3 MPa. Determine the mass using the compressibility factor. What is the error (%) if the ideal gas model is used? Homework Chapter3 3/1 Saturated water vapor at 200 kpa is in a constant pressure piston cylinder. At this state the piston is 0.1 m from the cylinder bottom and cylinder area is 0.25 m 2. The temperature is then changed to 200 o C. Find the work in the process. 3/2 A piston cylinder has 1.5 kg of air at 300 K and 150 kpa. It is now heated up in a two step process. First constant volume to 1000 K (state 2) then followed by a constant pressure process to 1500 K, state 3. Find the final volume and the work in the process. 3/3 A cylinder having a piston restrained by a linear spring (of spring constant 15 kn/m) contains 0.5 kg of saturated vapor water at 120 C, as shown in the figure below. Heat is transferred to the water, causing the piston to rise. If the piston cross-sectional area is 0.05 m 2, and the pressure varies linearly with volume until a final pressure of 500 kpa is reached. Find the final temperature in the cylinder and the heat transfer for the process.

3/4 A 25 kg steel tank initially at 10 o C is filled up with 100 kg of milk (assume properties as water) at 30 o C. The milk and the steel come to a uniform temperature of 5 o C in a storage room.

The air now cools to 400 K by heat transfer to the ambient. Find the final volume and pressure of the air (does it hit the stops?) and the work and heat transfer in the process.

2 3/4 A 25 kg steel tank initially at 10 o C is filled up with 100 kg of milk (assume properties as water) at 30 o C. The milk and the steel come to a uniform temperature of 5 o C in a storage room. How much heat transfer is needed for this process? 3/5 A piston/cylinder has 0.5 kg air at 2000 kpa, 1000 K, as shown in the figure. The cylinder has stops so V min = 0.03 m 3. The air now cools to 400 K by heat transfer to the ambient. Find the final volume and pressure of the air (does it hit the stops?) and the work and heat transfer in the process. Homework Chapter4 4/1 A compressor brings R-134a from 150 kpa, 10 o C to 1200 kpa, 50 o C. It is water cooled with a heat loss estimated as 40 kw and the shaft work input is measured to be 150 kw. How much is the mass flow rate through the compressor? 4/2 A heat exchanger, shown in the figure below, is used to cool an air flow from 800 K to 360 K, both states at 1 MPa. The coolant is a water flow at 15 C, 0.1 MPa. If the water leaves as saturated vapor, find the ratio of the mass flow rate of water to the mass flow rate of air. 4/3 A 1-m 3 tank contains ammonia at 150 kpa, 25 C. The tank is attached to a line flowing ammonia at 1200 kpa, 60 C. The valve is opened, and mass flows in until the tank is half full of liquid, by volume at 25 C. Calculate the heat transferred from the tank during this process.

3 Homework Chapter5 5/1 A car engine burns 5 kg fuel (equivalent to addition of Q H ) at 1500 K and rejects energy to the radiator and the exhaust at an average temperature of 750 K. If the fuel provides 40,000 kj/kg what is the maximum amount of work the engine can provide? 5/2 Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.25 kg liquid water at 10 o C. Assume the refrigerator works in a Carnot cycle between 8 o C and 35 o C with a motor-compressor of 750 W. How much time does it take if this is the only cooling load? Homework Chapter6 6/1 A cylinder containing R-134a at 10 C, 150 kpa, has an initial volume of 20 L. A piston compresses the R-134a in a reversible, isothermal process until it reaches the saturated vapor state. Calculate the required work and heat transfer to accomplish this process. 6/2 A 12 kg steel container has 0.2 kg superheated water vapor at 1000 kpa, both at 200 o C. The total mass is now cooled to ambient temperature 30 o C. How much heat transfer was taken out and what is the steel-water entropy change? 6/3 A piston/cylinder setup contains air at 100 kpa, 400 K which is compressed to a final pressure of 1000 kpa. Consider two different processes (i) a reversible adiabatic process and (ii) a reversible isothermal process. Show both processes in P-v and a T-s diagram. Find the final temperature and the specific work for both processes. 6/4 Ammonia is contained in a rigid sealed tank unknown quality at 0 o C. When heated in boiling water to 100 o C its pressure reaches 1200 kpa. Find the initial quality, the heat transfer to the ammonia and the total entropy generation.

4 Homework Chapter7 7/1 A compressor receives air at 290 K, 100 kpa and a shaft work of 5.5 kw from a gasoline engine. It should deliver a mass flow rate of 0.01 kg/s air to a pipeline. Find the maximum possible exit pressure of the compressor. 7/2 A mixing chamber receives 5 kg/min ammonia as saturated liquid at 20 C from one line and ammonia at 40 C, 250 kpa from another line through a valve. The chamber also receives 325 kj/min energy as heat transferred from a 40 C reservoir. This should produce saturated ammonia vapor at 20 C in the exit line. What is the mass flow rate in the second line and what is the total entropy generation in the process? 7/3 A turbine receives air at 1500 K, 1000 kpa and expands it to 100 kpa. The turbine has an isentropic efficiency of 85%. Find the actual turbine exit air temperature and the specific entropy increase in the actual turbine. Homework Chapter9 9/1 A steam power plant operating in an ideal Rankine cycle has a high pressure of 5 MPa and a low pressure of 15 kpa. The turbine exhaust state should have a quality of at least 95% and the turbine power generated should be 7.5 MW. Find the necessary boiler exit temperature and the total mass flow rate. 9/2 Consider an ideal steam reheat cycle where steam enters the high-pressure turbine at 3.0 MPa, 400 C, and then expands to 0.8 MPa. It is then reheated to 400 C and expands to 10 kpa in the low-pressure turbine. Calculate the cycle thermal efficiency and the moisture content of the steam leaving the low-pressure turbine. 9/3 A heat pump for heat upgrade uses ammonia with a low temperature of 25 o C and a high pressure of 5000 kpa. If it receives 1 MW of shaft work what is the rate of heat transfer at the high temperature?

5 Homework Chapter10 10/1 In a Brayton cycle the inlet is at 300 K, 100 kpa and the combustion adds 670 kj/kg. The maximum temperature is 1200 K due to material considerations. Find the maximum permissible compression ratio and for that the cycle efficiency using cold air properties. 10/2 Consider an ideal air-standard Brayton cycle with an ideal regenerator in which the air into the compressor is at 100 kpa, 20 C, and the pressure ratio across the compressor is 12:1. The maximum temperature in the cycle is 1100 C, and the air flow rate is 10 kg/s. Assume constant specific heat for the air, value from Table A.5. Determine the compressor work, the turbine work, and the thermal efficiency of the cycle. 10/3 A 4 stroke gasoline 4.2 L engine running at 2000 RPM has inlet state of 85 kpa, 280 K and after combustion it is 2000 K and the highest pressure is 5 MPa. Find the compression ratio, the cycle efficiency and the exhaust temperature. 10/4 A diesel engine has a compression ratio of 20:1 with an inlet of 95 kpa, 290 K, state 1, with volume 0.5 L. The maximum cycle temperature is 1800 K. Find the maximum pressure, the net specific work and the thermal efficiency. Homework Chapter11 11/1 A pipe flows 1.5 kg/s of a mixture with mass fractions of 40% carbon dioxide and 60% nitrogen at 400 kpa and 300 K, shown in Fig. below. Heating tape is wrapped around a section of pipe with insulation added, and 2 kw of electrical power is heating the pipe flow. Find the mixture exit temperature. -2kW

6 11/2 Natural gas as a mixture of 75% methane and 25% ethane by mass is flowing to a compressor at 17 C and 100 kpa. The reversible adiabatic compressor brings the flow to 250 kpa. Find the exit temperature and the needed work per kilogram of flow. 11/3 A room with 50 kg of dry air at 40% relative humidity, 20 C, is moistened by boiling water to a final state of 20 C and 100% humidity. How much water was added to the air? 11/4 In a ventilation system, inside air at 34 C and 70% relative humidity is blown through a channel, where it cools to 25 C with a flow rate of 0.75 kg/s dry air. Find the dew point of the inside air, the relative humidity at the end of the channel, and the heat transfer in the channel. 11/5 One means of air-conditioning hot summer air is by evaporative cooling, which is a process similar to the adiabatic saturation process. Consider outdoor ambient air at 35 C, 100 kpa, 30% relative humidity. What is the maximum amount of cooling that can be achieved by this technique? What disadvantage is there to this approach? Solve the problem using a first-law analysis.

Thermodynamics: Homework A Set 7 Jennifer West (2004)

Thermodynamics: Homework A Set 7 Jennifer West (2004) Problem 1 Water is the working fluid in a Carnot vapor power cycle. Saturated liquid enters the boiler at a pressure of 18 MPa, and saturated vapor