Friday, April 14, 2006

HW #7 - P #10 - Compression of an Ideal Gas in an Open and a Closed System - 6 pts

Helium gas is compressed from 90 kPa and 30°C to 450 kPa in a reversible, adiabatic process. Determine the final temperature and the work done, assuming the process takes place ...
a.) in a piston and cylinder device
b.)in a steady-flow compressor

HW #7 - P #9 - Entropy Change for an Incompressible Substance - 5 pts

A 20-kg aluminum block initially at 200°C is brought into contact with a 20-kg block of iron at 100°C in an insulated enclosure. Determine the final equilibrium temperature and the total entropy change for this process.

HW #7 - P #8 - 1st & 2nd Laws Applied to a Reversible, Adiabatic Process - 6 pts

A piston-and-cylinder device contains 5 kg of steam at 100°C with a quality of 50 percent. This steam undergoes two processes as follows:
1-2 Heat is transferred to the steam in a reversible manner while the temperature is held constant until the steam exists as a saturated vapor.
2-3 The steam expands in an adiabatic, reversible process until the pressure is 15 kPa.
a.) Sketch these processes with respect to the saturation lines on a single TS diagram
b.) Determine the heat added to the steam in process 1-2, in kJ
c.) Determine the work done by the steam in process 2-3, in kJ

HW #7 - P #7 - Maximum Work output from an Adiabatic Turbine - 5 pts

Steam enters an adiabatic turbine at 800 psia and 900°F and leaves at a pressure of 40 psia. Determine the maximum amount of work that can be delivered by this turbine.

HW #7 - P #6 - Entropy Generation in an Evaporator - 3 pts

Refrigerant-134a enters the coils of the evaporator of a refrigeration system as a saturated liquid / saturated vapor mixture at a pressure of 160 kPa. The refrigerant absorbs 180 kJ of heat from the cooled space, which is maintained at -5°C, and leaves as saturated vapor at the same pressure. For this process, determine ...
a.) the entropy change of the refrigerant
b.) the entropy change of the cooled space
c.) the total entropy change

HW #7 - P #5 - Efficiency and Reservoir Temperatures for Reversible and Irreversible Cycles - 6 pts

Complete the following involving reversible and irreversible cycles.

a.) Reversible and irreversible power cycles each discharge QC to a cold reservoir at TC and receive energy QH from hot reservoirs at TH and T'H, respectively. There are no other heat transfers involved. Show that T'H> TH.

b.) Reversible and irreversible heat pumpcycles each receive QC from a cold reservoir at TC and discharge QH to hot reservoirs at TH and T'H, respectively. There are no other heat transfers involved. Show that T'H < TH.

HW #7 - P #4 - Thermal Efficiency of an Internally Reversible HE with Multiple Heat Transfers - 4 pts

A system executes a power cycle while receiving 750 kJ by heat transfer at its boundary where the temperature is 1500 K and discharges 100 kJ by heat transfer at another portion of its boundary where its temperature is 500 K. Another heat transfer from the system occurs at a portion of the system boundary where the temperature of the system is 1000 K. No other heat transfer crosses the boundary of the system. If no internal irreversibilities are present, determine the thermal efficiency of the power cycle.

HW #7 - P #3 - Entropy Change in an Adiabatic Nozzle - 1 pt

Steam is accelerated as it flows through an actual adiabatic nozzle. The entropy of the steam at the nozzle exit will be (greater than, equal to, less than) the entropy at the nozzle inlet.

HW #7 - P #2 - Entropy Change in a Reversible, Isothermal Heating Process - 1 pt

The entropy of the working fluid of the ideal Carnot cycle (increases, decreases, remains the same) during the isothermal heat addition process.

HW #7 - P #1 - Entropy Change for an Adiabatic Process - 1 pt

A piston-and-cylinder device contains superheated steam. During an actual adiabatic process, the entropy of the steam will (never, sometimes, always) increase.

HW #6 - P #8 - Cost of Opening the Refrigerator Door - 8 pts

It is often stated that the refrigerator door should be opened as few times as possible for the shortest duration of time to save energy. Consider a household refrigerator whose interior volume is 0.9 m3 and average internal temperature is 4oC. At any given time, one-third of the refrigerated space is occupied by food items, and the remaining 0.6 m3 is filled with air. The average temperature and pressure in the kitchen are 20oC and 95 kPa, respectively. Also, the absolute humidity of the air in the kitchen and the air inthe refrigerator are 0.010 and 0.004 kg water / kg dry air (BDA), respectively. Thus, 0.006 kg of water vapor is condensed and removed from the air in the refrigerator for each kg of BDA that enters the refrigerator.

The refrigerator door is opened an average of 8 times a day. Each time the door is opened, half of the air volume in the refrigerator is replaced by the warmer, more humid kitchen air. If the refrigerator has a COP of 1.4 and the cost of electricity is $0.075 / kW-h, determine :
a.) the cost of the energy wasted per year as a result of opening the refrigerator door.
b.) What would your answer be if the kitchen air were very dry and thus a negligible amount of water condensed in the refrigerator ?

HW #6 - P #7 - Analysis of a Carnot Heat Pump - 6 pts

A Carnot heat pump is to be used to heat a house and maintain it at 20°C in winter. On a day when the average outdoor temperature remains at about 2°C, the house is estimated to lose heat at a rate of 82,000 kJ/h. If the heat pump consumes 8 kW of power while operating, determine ...
a.) how long the heat pump ran on that day
b.) the total heating costs, assuming an average price of 8.5¢/kWh for electricity
c.) the heating cost for the same day if resistance heating is used instead of a heat pump

HW #6 - P #6 - Analysis of a Carnot Refrigerator - 6 pts

A Carnot refrigerator operates in a room in which the temperature is 25°C. The refrigerator consumes 500 W of power when operating and has a COP of 4.5. Determine ...
a.) The rate of heat removal from the refrigerated space
b.) The temperature of the refrigerated space

HW #6 - P #5 - Analysis of a Carnot Heat Engine - 6 pts

A heat engine is operating on a Carnot cycle and has a thermal efficiency of 55 percent. The waste heat from this engine is rejected to a nearby lake at 60°F at a rate of 800 Btu/min. Determine...
a.) The power output of the engine
b.) The temperature of the source.

HW #6 - P #4 - Effect of Source and Sink Temperatures on HE Efficiency - 8 pts

A heat engine operates between a source at TH and a sink at TC. Heat is supplied to the heat engine at a steady rate of 1200 kJ/min. Study the effects of TH and TC on the maximum power produced and the maximum cycle efficiency. For TC = 25oC, let TH vary from 300oC to 1000oC. Create plots of Wcycle and ηth as functions of TH. For TH = 550oC, let TC vary from 0oC to 50oC. Create plots of Wcycle and ηth as functions of TC. Discuss the results.

HW #6 - P #3 - A Reversible HE Used to Drive a Reversible Heat Pump - 6 pts

A reversible power cycle receives QH from a hot reservoir at TH and rejects Qsurr to the surroundings at T0. The work developed by the power cycle is used to drive a reversible refrigeration cycle that removes QC from a cold reservoir at TC and rejects heat to the same surroundings T0.
a.) Develop an expression for the ratio QC / QH in terms of the temperature ratios TH / T0 and TC / T0.
b.) Plot QC / QH versus TH / T0 for TC / T0 = 0.85, 0.90 and 0.95.
c.) Plot QC / QH versus TC / T0 for TH / T0 = 2, 3 and 4.

HW #6 - P #2 - Reversible, Irreversible and Impossible Power Cycles - 8 pts

A power cycle operating between two reservoirs receives QH from a hot reservoir at TH = 2000 K and rejects QC to a cold reservoir at TC = 400 K. For each of the following cases, determine whether the cycle is reversible, irreversible or impossible.
a.) QH = 1200 kJ and Wcycle = 1020 kJ
b.) QH = 1200 kJ and QC = 240 kJ
c.) QC = 600 kJ and Wcycle = 1400 kJ
d.) η = 40%

HW #6 - P #1 - "Show That" Problem Using the K-P Statement of the 2nd Law - 6 pts

Using the Kelvin-Planck Statement of the Second Law of Thermodynamics, demonstrate the following corollaries.
a.) The COP of an irreversible heat pump cycle is always less than the COP of a reversible heat pump cycle when both cycles exchange heat with the same two reservoirs.
b.) All reversible heat pump cycles operating between the same two reservoirs have the same COP.

HW #5 - P #10 - Filling a Balloon with Helium - 10 pts

A balloon initially contains 65 m3 of helium gas at atmospheric conditions of 100 kPa and 22oC. The balloon is connected by a valve to a large reservoir that supplies helium gas at 150 kPa and 25oC. Now, the valve is opened and helium is alowed to enter the balloon until pressure equilibrium with the helium at the supply line is reached. The material of the balloon is such that its volume increases linearly with pressure. If no heat transfer takes place during this process, determine the final temperature of the helium in the balloon.

HW #5 - P #9 - Operation of a Pressure Cooker - 8 pts

A 4 L pressure cooker has an operating pressure of 175 kPa. Initially, one-half of the volume is filled with liquid and the other half with vapor. If it is desired that the pressure cooker not run out of water for one hour, determine the highest rate of heat transfer allowed.

HW #5 - P #8 - Temperature Rise and Efficiency of a Pump - 6 pts

The pump of a water distribution system is powered by a 15-kW electric motor whose efficiency is 90 percent. The water flow rate through the pump is 50 L/s. The diameters of the inlet and outlet pipes are the same, and the elevation difference across the pump is negligible. If the pressures at the inlet and outlet of the pump are measured to be 100 kPa and 300 kPa (absolute), respectively, determine...
a.) The mechanical efficiency of the pump
b.) The temperature rise of water as it flows through the pump due to the mechanical inefficiency

HW #5 - P #7 - Steam Condensation Using Cooling Water - 6 pts

Steam enters the condenser of a steam power plant at 20 kPa and a quality of 95 percent with a mass flow rate of 20,000 kg/h. It is to be cooled by water from a nearby river by circulating the water through the tubes within the condenser. To prevent thermal pollution, the river water is not allowed to experience a temperature rise above 10°C. If the steam is to leave the condenser as saturated liquid at 20 kPa, determine the mass flow rate of the cooling water required.

HW #5 - P #6 - An Ideal, Adiabatic Open Feedwater Heater - 6 pts

In steam power plants, open feedwater heaters are frequently utilized to heat the feedwater by mixing it with steam bled off the turbine at some intermediate stage. Consider an open feedwater heater that operates at a pressure of 1000 kPa. Feedwater at 50°C and 1000 kPa is to be heated with superheated steam at 200°C and 1000 kPa. In an ideal feedwater heater, the mixture leaves the heater as saturated liquid at the feedwater pressure. Determine the ratio of the mass flow rates of the feedwater and the superheated vapor for this case.

HW #5 - P #4 - Steady Flow Through an Air Compressor - 6 pts

Air enters the compressor of a gas-turbine plant at ambient conditions of
100 kPa and 25°C with a low velocity and exits at 1 MPa and 347°C with a
velocity of 90 m/s. The compressor is cooled at a rate of 1500 kJ/min, and
the power input to the compressor is 250 kW. Determine the mass flow rate of
air through the compressor.

HW #5 - P #3 - Steady Flow Through an Adiabatic Steam Turbine - 6 pts

Steam flows steadily through an adiabatic turbine. The inlet conditions of
the steam are 10 MPa, 450°C, and 80 m/s, and the exit conditions are 10 kPa,
92 percent quality, and 50 m/s. The mass flow rate of the steam is 12 kg/s.
a.) The change in kinetic energy
b.) The power output
c.) The turbine inlet area

HW #5 - P #2 - Outlet Temperature and Velocity in an Adiabatic Diffuser - 6 pts

Air at 13 psia and 20°F enters an adiabatic diffuser steadily with a
velocity of 600 ft/s and leaves with a low velocity at a pressure of 14.5
psia. The exit area of the diffuser is 5 times the inlet area. Determine...
a.) The exit temperature
b.) The exit velocity of the air

HW #5 - P #1 - Steady Flow Through a Nozzle - 6 pts

Steam at 5 MPa and 400°C enters a nozzle steadily with a velocity of 80 m/s,
and it leaves at 2 MPa and 300°C. The inlet area of the nozzle is 50 cm2,
and heat is being lost at a rate of 120 kJ/s. Determine...
a.) The mass flow rate of the steam
b.) The exit velocity of the steam
c.) The exit area of the nozzle

HW #5 - P #5 - Temperature Drop in an Adiabatic Throttling Valve - 6 pts

Refrigerant-134a is throttled from the saturated liquid state at 700 kPa to a pressure of 160 kPa. Determine the temperature drop during this process and the final specific volume of the refrigerant.

Tuesday, April 11, 2006

HW #4 - P #11 - Coefficient of Performance of a Household Heat Pump

A heat pump used to heat a house runs about one-third of the time. The house is losing heat at an average rate of 22,000 kJ/h. If the COP of the heat pump is 2.8, determine the power the heat pump draws when running.

HW #4 - P #10 - Coefficient of Performance of a Household Refrigerator

A household refrigerator with a COP of 1.2 removes heat from the refrigerated space at a rate of 60 kJ/min. Determine (a) the electric power consumed by the refrigerator and (b) the rate of heat transfer to the kitchen air.

HW #4 - P #9 - Thermal Efficiency of an Automobile Engine

An automobile engine consumes fuel at a rate of 28 L/h and delivers 60 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm3, determine the thermal efficiency of this engine.

HW #4 - P #8 - Thermal Efficiency of a Steam Power Plant

A 600-MW steam power plant, which is cooled by a nearby river, has a thermal efficiency of 40 percent. Determine the rate of heat transfer to the river water. Will the actual heat transfer rate be higher or lower than this value? Why?

HW #4 - P #7 - 1st Law Applied to Cooking an Egg

An ordinary egg can be approximated as a 5.5-cm-diameter sphere. The egg is initially at a uniform temperature of 8°C and is dropped into boiling water at 97°C. Taking the properties of the egg to be = 1020 kg/m3 and cP = 3.32 kJ/kg · °C, determine how much heat is transferred to the egg by the time the average temperature of the egg rises to 80°C.

HW #4 - P #6 - Electrical Work and the 1st Law

A mass of 15 kg of air in a piston-and-cylinder device is heated from 25 to 77°C by passing current through a resistance heater inside the cylinder. The pressure inside the cylinder is held constant at 300 kPa during the process, and a heat loss of 60 kJ occurs. Determine the electric energy supplied, in kWh.

HW #4 - P #5 - Two Step Expansion with Stops

A piston-and-cylinder device initially contains 0.8 m3 of saturated water vapor at 250 kPa. At this state, the piston is resting on a set of stops, and the mass of the piston is such that a pressure of 300 kPa is required to move it. Heat is now slowly transferred to the steam until the volume doubles. Show the process on a PV diagram with respect to saturation lines and determine...
a.) The final temperature
b.) The work done during this process
c.) The total heat transfer

HW #4 - P #4 - Conduction and Convection Heat Transfer

A flat surface is covered with insulation with a thermal conductivity of 0.08 W/m-K. The temperature at the interface between the surface and the insulation is 300°C. The outside of the insulation is exposed to air at 30°C and the convective heat transfer coefficient between the insulation and the air is 10 W/m2-K. Ignoring radiation, determine the minimum thickness of insulation in meters such that the outside surface of the insulation is not hotter than 60°C at steady-state.

HW #4 - P #3 - Convection and Radiation Heat Transfer

A 5cm diameter spherical ball whose surface is maintained at a temperature of 70oC is suspended in the middle of a room at 20oC. If the convection heat transfer coefficient is 15 W/m2-oC and the emissivity of the surface is 0.8, determine the total rate of heat transfer from the ball.

HW #4 - P #2 - Two Step Expansion with a Linear Spring

A piston-and-cylinder device contains 50 kg of water at 250 kPa and 25°C.
The cross-sectional area of the piston is 0.1 m2. Heat is now transferred to
the water, causing part of it to evaporate and expand. When the volume reaches 0.2 m3, the piston reaches a linear spring whose spring constant is 100 kN/m. More heat is transferred to the water until the piston rises 20 cm more. Determine...
a.) The final pressure and temperature
b.) The work done during this process
c.) Show the process on a P-V diagram

HW #4 - P #1 - Boundary Work as a Gas Expands

During an expansion process, the pressure of a gas changes from 15 to 100 psia according to the relation P = aV + b, where a = 5 psia/ft3 and b is a constant. If the initial volume of the gas is 7 ft3, calculate the boundary work done during the process.

Monday, April 10, 2006

HW #3 - P7 - Hypothetical Process Paths and the Latent Heat of Vaporization

Use the hypothetical process path shown here to help you determine the change in enthalpy in Joules for 20.0 g of heptane (C7H16) as it changes from a saturated liquid at 300 K to a temperature of 370 K and a pressure of 58.7 kPa. Calculate the DH for each step in the path. Do not use tables of thermodynamic properties, except to check your answers. Instead, use the Antoine Equation to estimate the heat of vaporization of heptane at 300 K. Use the average heat capacity of heptane gas over the temperature range of interest. Assume heptane gas is an ideal gas at the relevant temperatures and pressures.

HW #3 - P6 - Vapor Pressure of Solids and the Clausius-Clapeyron Equation

Using the Clapeyron-Clausius equation and the triple- point data of water, estimate the sublimation pressure of water at -30°C and compare to the actual value of 38.02 Pa. ΔHsub = 2838.4 kJ/kg .

HW #3 - P5 - Using Vapor Pressure Data to Estimate ΔHvap

Using the Clapeyron equation, estimate the enthalpy of vaporization of steam at 300 kPa, and compare it to the tabulated value.

HW #3 - P4 - Determining Internal Energy Change Using Heat Capacity Polynomials

Determine the change in the specific internal energy of hydrogen (H2), in kJ/kg, as it is heated from 400 to 1000 K, using:
a.) the empirical specific heat equation (Shomate Equation) from the back of your book.
b.) The Cv(IG) value at the average temperature. (Use theat capacity polynomial to determine this CoV value.)
c.) The Cv(IG)value at room temperature, 25oC. (Use theat capacity polynomial to determine this Cv(IG)value.)

HW #3 - P3 - Determining Enthalpy Change Using Heat Capacity Polynomials

Determine the change in the specific enthalpy of nitrogen (N2), in kJ/kg, as it is heated from 600 to 1000 K, using:
a.) the empirical specific heat equation (Shomate Equation) from the back of your book.
b.) The Cp IG value at the average temperature. (Use the heat capacity polynomial to determine this Cp IG value.)
c.) The Cp IG value at room temperature, 25oC. (Use theat capacity polynomial to determine this Cp IG value.)

HW #3 - P2 - R-134a Table Fundamentals

Complete this table for refrigerant-134a.

T(oF) P (psia) H (Btu/lbm) x Phase Description
a.) 80 141.768
b.) 15 0.6
c.) 10 70
d.) 180 193.228
e.) 110 1.0

HW #3 - P1 - Steam Table Fundamentals

Complete the blank cells in the following table of properties of steam. In
the last column describe the condition of steam as compressed liquid,
saturated mixture, superheated vapor, or insufficient information; and, if
applicable, give the quality.

T(oC) P (kPa) V (m3/kg) U (kJ/kg) Quality
x Phase Description
a.) 30 200
b.) 130 270.28
c.) 400 1.5493
d.) 300 0.500
e.) 500 3084

Saturday, April 01, 2006

HW #2 - P #8 - Relative Humidity

A thermos bottle is half-filled with water and is left open to the atmospheric air at 70°F and 35% relative humidity. If heat transfer to the water through the thermos walls and the free surface is negligible, determine the temperature of water when phase equilibrium is established.

HW #2 - P #7 - Vapor Pressure of Water

During a hot summer day at the beach when the air temperature is 30°C, someone claims the vapor pressure in the air to be 5.2 kPa. Is this claim reasonable?

HW #2 - P #6 - An Application of Equations of State

A 0.016773 m3 tank contains 1 kg of R-134a at 110oC. Determine the pressure of the refrigerant using:
a.) the ideal gas EOS
b.) the generalized compressibility chart
c.) the refrigerant tables
d.) van der Waals EOS
e.) Soave-Redlich-Kwong EOS

HW #2 - P #5 - PVT Relationship Applied to an Automobile Tire

The pressure in an automobile tire depends on the temperature of the air in the tire. When the air temperature is 25°C, the pressure gage reads 210 kPa. If the volume of the tire is 0.025 m3, determine the pressure rise in the tire when the air temperature in the tire rises to 50°C. Also, determine the amount of air that must be bled off to restore pressure to its original value at this temperature. Assume atmospheric pressure is 100 kPa.

HW #2 - P #4 - Isochoric Condensation of Water Vapor

Superheated water vapor at 180 psia and 500°F is allowed to cool at constant volume until the temperature drops to 250°F. At the final state, determine...
a.) the pressure
b.) the quality
c.) the enthalpy
d.) Show the process on a TV diagram with respect to saturation curves

HW #2 - P #3 - Isobaric Heating of Water and Steam

A piston-and-cylinder device contains 0.1 m3 of liquid water and 0.9 m3 of water vapor in equilibrium at 800 kPa. Heat is transferred at constant pressure until the temperature reaches 350°C.
a.) What is the initial temperature of the water?
b.) Determine the total mass of the water.
c.) Calculate the final volume.
d.) Show the process on a PV diagram with respect to saturation curves.