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thermodynamics

Thermodynamics for Engineers 1st edition Kenneth A. Kroos, Merle C. Potter - Solutions

Fifteen thousand pounds of superheated steam enter a turbine each hour at 1000 psia and 1000° F and leave the turbine at 5 psia as saturated vapor producing 2000 hp. Calculate the rate of entropy change in the steam and in the universe if the surroundings are at 70°F.
The insulated turbine in the Rankine cycle in Fig. 6.56, operating with water, produces 3000 kW of power. Determine the entropy change across each device.Figure 656
Water at atmospheric pressure and 180° F enters a mixing chamber at a flow rate of 80 gpm. Cold water enters the mixing chamber at 40° F at a flow rate of 120 gpm. Calculate the temperature of the water leaving the mixing chamber and the rate of change of entropy for this insulated chamber.
The boiler in a power plant heats water to a temperature near 600 8 C before it enters the turbine. The water is preheated by mixing it with superheated steam extracted from the turbine before it enters the boiler, resulting in less fuel used by the boiler. The insulated preheater is shown in Fig.
Steam at 600 kPa and 350° C enters an adiabatic turbine at a flow rate of 20 kg/s. It leaves the turbine at a pressure of 40 kPa as a saturated vapor. Calculate the power produced by this turbine and the isentropic efficiency of the turbine.
Air enters an adiabatic gas turbine at 600 kPa and 400° C. It leaves the turbine at atmospheric pressure and a temperature of 140° C. Calculate the specific work output and the isentropic efficiency of this turbine. Assume constant specific heats.
For the adiabatic steam turbine of Fig. 6.58, calculate the isentropic efficiency ifa) x2 = 0.9,b) x2 = 1.0,c) T2 = 50° C,d) T2 = 60° C.Figure 6.58
An insulated steam turbine accepts 35 lbm/s at 2000 psia and 1000° F and discharges it at 2 psia. Determine the power produced and the efficiency if the exit quality is a) x2 = 0.82, b) x2 = 0.90, c) x2 = 1.0.
An insulated steam turbine produces 8000 hp by accepting 30 000 kg of steam at 10 MPa each hour and discharging the steam at 20 kPa with a quality of 85%. Determine the inlet temperature and the turbine efficiency.
An air compressor has an isentropic efficiency of 0.88. If air at 100 kPa and 25ºC and a mass ﬂow rate of 20 000 kg/hr is compressed to 500 kPa, what work must be supplied to the compressor? Assume constant specific heats.
Saturated ammonia vapor is compressed as shown in Fig. 6.59. Calculate the horsepower input if the compressor's adiabatic efficiency isa) 80%,b) 90%,c) 100%.Figure 6.59
Saturated R134a vapor is to be compressed from 20 psia to 400 psia in a compressor rated at 86% efficiency. Determine the horsepower requirement if the mass flow rate is 400 lbm each hour.
Water enters a pump at 80 kPa and leaves the pump at 6 MPa. The mass flow rate through the pump is 90 kg/min. If the pump requires 15 hp, calculate the pump efficiency.
The pump of Fig. 6.60 is used in a power plant to increase the low pressure of saturated liquid water exiting a condenser to a high pressure entering a boiler. Estimate the efficiency of the pump if it accepts 2400 kg of water each minute at 10 kPa and discharges it at 8 MPa while consuming 4000
Determine the horsepower requirement of a pump that increases the pressure of water from 20 kPa to 5 MPa if it is 88% efficient and pumps 340 000 gallons of water each day.
Air enters a nozzle at 20 m/s and 25° C with a pressure of 140 kPa. If the exit pressure is 100 kPa and the nozzle is 96% efficient, estimate the exiting velocity.
The air in the constant-pressure cylinder of Fig. 6.37 is initially at 400 8 C and 120 kPa. It is cooled until its temperature is 40 8 C. The surroundings are at 20 8 C. The entropy generated during this process is nearest:(A) 0.463 kJ/kg ˆ™ K(B) 0.591 kJ/kg ˆ™ K(C) 0.766 kJ/kg
Air enters a nozzle at 106 m/s and 80° C with a pressure of 120 kPa. If the exit pressure is 100 kPa and the nozzle is 92% efficient, estimate the exiting velocity and temperature.
A steam generator produces superheated steam at a rate of 140 kg/min, a temperature of 500° C, and a pressure of 5 MPa. What is the maximum amount of power that could be obtained using this steam? Use the standard dead state.
Steam enters a turbine at 10 MPa and 600° C and exits at 20 kPa with a quality of 95%. Determine the irreversibility of this process.
What is the exergy of air at 300° C and 600 kPa if the dead state is 20° C and 101 kPa? a) Assume constant specific heats and b) Use Table F-1.
R134a enters a compressor at 30 psia and 10 ° F at a flow rate of 40 gpm, and leaves with a temperature of 300 ° F and a pressure of 160 psia. What is the rate of change of exergy for this device?
Two kilograms of steam enter a turbine each second at 600° C and 4 MPa and leave as saturated vapor at 20 kPa while 100 kJ/s of heat leave the turbine. The surroundings are at 25° C. The entropy production is nearest: (A) 1.42 kJ/K ∙ s (B) 1.08 kJ/K ∙ s (C) 0.63 kJ/K ∙ s (D) 0.34 kJ/K ∙ s
Apply Eqs. 7.7 and 7.10 directly to Eqs. 7.1 and 7.2 and derive the relations of Eqs. 7.11 and 7.12. Eq. 7.1 du = Tds - Pdv Eq. 7.2 dh = Tds + vdP Eq. 7.7 dz = (∂z/∂x)y dx + (∂z/∂y)x dy Eq. 7.11 (∂T/∂v)s = - (∂P/∂s)v Eq. 7.12 (∂T/∂P)s = (∂v/∂s)P
Apply Eqs. 7.7 and 7.10 directly to Eqs. 7.5 and 7.6 and derive the relations of Eqs. 7.13 and 7.14. Eq. 7.5 dα = Pdv - sdT Eq. 7.6 dg = vdP - sdT Eq. 7.10 dz = (∂z / ∂x)y dx + (∂z / ∂y)x dy Eq. 7.13 (∂P/∂T)v = (∂s/∂v)T Eq. 7.14 (∂v/∂T)P = - (∂s/∂P)T
Apply Eq. 7.7 directly to Eqs. 7.1 and 7.2 and derive the relations of Eqs. 7.15 and 7.16. Eq. 7.1 du = Tds - Pdv Eq. 7.2 dh = Tds + vdP Eq. 7.7 dz = (∂z/∂x)y dx + (∂z/∂y)x dy Eq. 7.15 (∂u/∂s)v = T and (∂u/∂v)x = - P Eq. 7.16 (∂g/∂P)T = v and (∂g/∂T)P = - s
An ideal gas undergoes a process from state 1 to state 2. For the following data, approximate the change in specific entropy for this process using Eq. 7.13.
An ideal gas undergoes a process from state 1 to state 2. For the data shown below, approximate the change in specific entropy for this process using Eq. 7.11.
Verify Eq. 7.12, which is (∂T/ ∂P) s = (∂V/ ∂s)P, using the properties of steam at 1 MPa and 400° C.
R134a exists at 500 kPa and 100° C. Verify Eq. 7.14, which is (∂V/ ∂T)P = 2 (∂s / ∂P)T, using a) The values in Table D-3 b) The IRC Calculator.
Verify Eq. 7.14, which is (∂V/ ∂T)P = - (∂s / ∂P)T, using the properties of R134a at 300° F and 160 psia.
Verify, using ammonia at 200 kPa and 40° C, that (∂h / ∂s)P = T is indeed true using the values in Table E-2.
Verify, using steam at 800 kPa and 400° C, that (∂h / ∂s)P = T is indeed true using a) The values in Table C-3 b) The IRC Calculator.
Verify, using steam at 800 psia and 800° F, that (∂u / ∂s) = T is indeed true. Use the IRC Calculator.
Show that saturated water vapor at 20 kPa can be treated as an ideal gas (compare v = RT/P with vg from Table C-2). Could saturated water vapor at 100 kPa be treated as an ideal gas?
Using the pressure, temperature, and specific volume found in Table C-1, determine hfg for steam at 300° C using the Clapeyron equation. Also determine sfg. Calculate the errors assuming the values obtained in Table C-1 are accurate.
Using the pressure, temperature, and specific volume found in Table D-1, determine hfg for R134a at 60° F by applying the Clapeyron equation. Also determine sfg. Calculate the errors assuming the values obtained in Table D-1 are accurate.
The steam table C-2E has a low pressure of 1 psia, unlike Table C-2, which has a much lower pressure of 0.611 kPa. A need is expressed for the saturation temperature of steam below 1 psia; suppose that only Table C-2E is available. Estimate the saturation temperature of steam at a) 0.1 psia, b) 0.2
Determine an expression for the quantities in the brackets of Eqs. 7.33 and 7.39 for an ideal gas for which Pv = RT
Assume an ideal gas with constant specific heats for which Pv = RT and determine expressions for ΔS using Eqs. 7.41 and 7.42.
Find the expression for the change in internal energy Δu for a gas obeying the equation of state P = RT/(v - b) - a/v2 (the van der Waals equation) assuming constant specific heats.
Find the expression for the change in enthalpy Δh for a gas obeying the equation of state P = RT / (v - b) - a/v2 (the van der Waals equation) assuming constant specific heats.
Find a relationship for Cp - Cp for a gas for which the van der Waals equation of state P = RT / (v - b) - a/v2 is applicable. Then let a = b = 0 and show that Cp - Cv = R.
Air undergoes an isothermal process at 100° C from 200 kPa to 6000 kPa. Calculate the enthalpy and entropy changes using the van der Waals equation of state P = RT / (v - b) - a/v2. Assume that the specific heat depends on temperature only. Then compare the results with those assuming constant
A 50-kg block of aluminum experiences a pressure change from 100 kPa to 50 MPa, while the temperature increases from 50ºC to 100ºC. Estimate its change in entropy. Use b = 7 × 10-5 K-1, Cp = 0.9 kJ/kg∙°C, and r = 2700 kg/m3. What is the contribution due to the pressure increase?
Estimate β and B for water at 10 MPa and 40° C and then find the difference Cp - Cv.
Estimate β and B for water at 1000 psia and 100° F and then find the difference Cp - Cv.
Estimate β and B for R134a at 800 kPa and 0° C and then find the difference Cp - Cv. Use the IRC Calculator.
Estimate the Joule-Thomson coefficient for R134a at 350 kPa and x = 0. Then predict the exiting temperature from the valve of Fig. 7.5 if the entering pressure drops to 100 kPa froma) 400 kPa and 8°C,b) 600 kPa and 21°C,c) 800 kPa and 31°C. Use the IRC Calculator.Figure 7.5
Estimate the Joule-Thomson coefficient for R134a at 1000 kPa and x = 0; then predict the exiting temperature from a valve if the pressure drops to 100 kPa from 2000 kPa and the entrance temperature of 67°C. Use the IRC Calculator.
Estimate the Joule-Thomson coefficient for air entering the valve of Fig. 7.6 at 1200 kPa and 400°C and show that the temperature does not significantly change when the pressure drops to 100 kPa.Figure 7.6
Estimate the Joule-Thomson coefficient of steam at 4 MPa and 400°C, and then estimate the value for Cp at that state using Eq. 7.53. Compare with the value found by using Cp = (∂h / ∂T)P.
Estimate the Joule-Thomson coefficient of steam at 800 psia and 800°F, and then estimate the value for Cp at that state using Eq. 7.53. Compare with the value found by using Cp = (∂h / ∂T)P.
Calculate the change in enthalpy of air using both the ideal-gas table and the enthalpy departure chart if its state changes from: a) 260 K and 900 kPa to 820 K and 4 Mpa b) 360 K and 900 kPa to 220 K and 8 MPa c) 300 K and 200 kPa to 600 K and 10 MPa
Calculate the change in enthalpy of carbon dioxide using both the ideal-gas table and the enthalpy departure chart if its state changes from: a) 320 K and 800 Pa to 300 K and 6 MPa b) 400 K and 2 MPa to 400 K and 12 Mpa c) 500 K and 400 kPa to 900 K and 10 MPa
Calculate the change in entropy of air using both the ideal-gas table and the entropy departure chart if its state changes from: a) 520° R and 180 psia to 1600° R and 1000 psia b) 600°R and 250 psia to 1800°R and 3000 psia c) 400° R and 100 psia to 440° R and 4000 psia
Calculate the change in the entropy of nitrogen using both the ideal-gas table and the entropy departure chart if its state changes from: a) 260 K and 900 kPa to 800 K and 4 MPa b) 350 K and 1200 kPa to 700 K and 8 MPa c) 500 K and 1800 kPa to 220 K and 10 MPa
Air undergoes a process from state 1 at 400 K and 200 kPa to state 2 at 900 K and 12 MPa. Estimate the change in enthalpy and entropy: i) Assuming the air is an ideal gas with constant specific heats from Table B-2 ii) Assuming the air is an ideal-gas with constant specific heats interpolated from
Air undergoes a process from state 1 at 220 K and 200 kPa to state 2 at 300 K and 10 MPa. Estimate the change in enthalpy and entropy: i) Assuming the air is an ideal-gas with constant specific heats from Table B-2 ii) Using the ideal-gas tables in the Appendix iii) Using the equations of Section
Nitrogen undergoes a process from state 1 at 220 K and 2 MPa to state 2 at 280 K and 20 MPa. Estimate the change in enthalpy and entropy: i) Assuming the nitrogen is an ideal gas with constant specific heats from Table B-2 ii) Assuming the nitrogen is an ideal gas with constant specific heats
Carbon dioxide undergoes a process from state 1 at 640°R and 900 psia to state 2 at 900° R and 3000 psia. Estimate the change in enthalpy, internal energy, and entropy: i) Assuming the carbon dioxide is an ideal-gas with constant specific heats from Table B-2E ii) Using the ideal-gas tables in
Determine the maximum power produced by the adiabatic turbine of Fig. 7.7 that accepts 4 kg/s of air at 10 MPa and 1100 K and exhausts the air to the atmosphere at 100 kPa.i) Use the ideal-gas tableii) account for real-gas behavior.Figure 7.7
Calculate the minimum power required to compress 2 kg/s of nitrogen from 100 kPa and 300 K to 8 MPa assuming an adiabatic process. i) Use the ideal-gas table ii) Account for real-gas behavior.
A rigid volume contains air at 300 K and 400 kPa. If the temperature is raised to 1200 K, determine the final pressure and the heat transfer i) Assuming ideal-gas behavior ii) Accounting for real-gas effects.
Nitrogen enters a compressor at 27°C and 1.5 MPa and exits at 480 K and 15 MPa. If the mass flux is 2 kg/s, determine the enthalpy change, the entropy change, and the power required if the heat loss is 20 kJ/s.
Air is compressed isothermally from 20 psia and 100°F to 1200 psia, as shown in Fig. 7.8. Calculate the enthalpy change, the entropy change, and the work required if the heat loss is 80 Btu/lbm.Figure 7.8
Use the differential form for dv (see Eq. 7.7) assuming v = RT/P and find the change in the specific volume Δv of air if the pressure and temperature change from 200 kPa and 100° C to 210 kPa and 120° C. Compare with Δv using the ideal-gas law directly.
Use the differential form for dP (see Eq. 7.7) assuming P = RT/ v and find the change in the pressure of air if the specific volume and temperature change from 0.5 m3/kg and 80° C to 0.52 m3/kg and 70° C. Compare with ΔP using the ideal-gas law directly.
The component that results in a relatively low Rankine cycle efficiency is: (A) The condenser (B) The turbine (C) The boiler (D) The pump
A reheater that extracts steam from the turbine at 1.0 MPa is added to the cycle of Fig. 8.29 and reheats it to 600°C at constant pressure. Such a device increases the cycle efficiency to:(A) 51%(B) 49%(C) 47%(D) 45%Figure 8.29Figure 8.30
If 50% of the heat from the condenser of Fig. 8.29 is used to heat buildings, the utilization factor « of the cycle is nearest:(A) 71%(B) 67%(C) 64%(D) 61%Figure 8.29Figure 8.30
An open feedwater heater extracts steam from the turbine of Fig. 8.29 at 1.0 MPa and 200 8 C. Saturated liquid water leaves the heater. The mass flux of the extracted steam should be nearest:(A) 2.1 kg/s(B) 1.9 kg/s(C) 1.7 kg/s(D) 1.5 kg/sFigure 8.29Figure 8.30
An ideal Rankine power cycle is shown in Fig. 8.31. Steam leaves the steam generator at 4 MPa and 500°C with a mass flow rate of 8 kg/s. The steam leaves the turbine at 40 kPa. Sketch the cycle on a T-s diagram; then calculate:i) The power output of the turbineii) The rate of heat loss from the
Work Problem 8.13, retaining all quantities except with the following turbine exit pressure:a) 50 kPab) 30 kPac) 20 kPad) 10 kPaRework Problem 8.13An ideal Rankine power cycle is shown in Fig. 8.31. Steam leaves the steam generator at 4 MPa and 500°C with a mass flow rate of 8 kg/s. The steam
Work Problem 8.13, retaining all quantities except with the following turbine inlet conditions:a) 4 MPa, 400°Cb) 4 MPa, 600°Cc) 4 MPa, 700°Cd) 4 MPa, 800°CRework Problem 8.13An ideal Rankine power cycle is shown in Fig. 8.31. Steam leaves the steam generator at 4 MPa and 500°C
Work Problem 8.13, retaining all quantities except with the following turbine inlet conditions:a) 6 MPa, 600°Cb) 10 MPa, 600°Cc) 20 MPa, 600°Cd) 30 MPa, 600°CRework Problem 8.13An ideal Rankine power cycle is shown in Fig. 8.31. Steam leaves the steam generator at 4 MPa and
An ideal Rankine power cycle shown in Fig. 8.32 has a boiler that produces steam at 600 psia and 900°F with a mass flux of 18 lbm/s. The steam leaving the turbine has a pressure of 10 psia. Sketch this cycle on a T-s diagram and then calculate:i) The power output of the turbineii) The rate of
Work Problem 8.17, retaining all quantities except with the following turbine exit pressure:a) 10 psiab) 8 psiac) 4 psiad) 2 psiaRework Problem 8.17An ideal Rankine power cycle shown in Fig. 8.32 has a boiler that produces steam at 600 psia and 900°F with a mass flux of 18 lbm/s. The steam
Work Problem 8.17, retaining all quantities except with the following turbine inlet conditions:a) 600 psia, 700°Fb) 600 psi, 1000°Fc) 600 psi, 1200°Fd) 600 psi, 1400°FRework Problem 8.17An ideal Rankine power cycle shown in Fig. 8.32 has a boiler that produces steam at 600 psia and
Regeneration allows: (A) The condenser to accept steam at a lower quality (B) The turbine energy to be restored (C) The boiler water to be preheated (D) The pump to pressurize the water before it enters the boiler
Work Problem 8.17, retaining all quantities except with the following turbine inlet conditions:a) 800 psia, 900 °Fb) 1200 psia, 900 °Fc) 1600 psia, 900 °Fd) 4000 psia, 900 °FRework Problem 8.17An ideal Rankine power cycle shown in Fig. 8.32 has a boiler that produces steam at 600
For Problem 8.13 assume that the turbine has an efficiency of 90% and the pump has an efficiency of 85%. Calculate the power output and efficiency of the cycle.
For turbine efficiencies of i) 0.82, ii) 0.84, iii) 0.86, iv) 0.88 in Problem 8.13 with a pump efficiency of 80%, calculate the cycle efficiency. State your observation of the thermodynamic efficiency of the cycle as a function of the turbine efficiency.
A geothermal energy source is to be used in the operation of a Rankine power cycle using R134a as the working fluid. The R134a is to leave the heater at 60 psia and 200°F and the ideal turbine at 2 psia. Sketch a T- s diagram. For a mass flow rate of 5 lbm/s, calculate: i) The maximum power to be
An ideal Rankine power cycle with reheat is shown in Fig. 8.33. Steam leaves the boiler at 8 MPa and 700°C with a mass flux of 20 kg/s. It leaves the high-pressure turbine (HPT) at 1 MPa and is reheated to 700°C before being sent back to the low-pressure turbine (LPT). The steam then enters
Work Problem 8.24 with the following turbine reheat intercept pressure:a) 200 kPa andb) 600 kPa.An ideal Rankine power cycle with reheat is shown in Fig. 8.33. Steam leaves the boiler at 8 MPa and 700°C with a mass flux of 20 kg/s. It leaves the high-pressure turbine (HPT) at 1 MPa and is
Work Problem 8.24 with a condenser pressure ofa) 10 kPab) 5 kPa.An ideal Rankine power cycle with reheat is shown in Fig. 8.33. Steam leaves the boiler at 8 MPa and 700°C with a mass flux of 20 kg/s. It leaves the high-pressure turbine (HPT) at 1 MPa and is reheated to 700°C before being
Determine the state (quality, or temperature if superheat) of the steam exiting the turbine of Problem 8.24 if the efficiency of both stages of the turbine is a) 92% b) 86%.
In the ideal Rankine power cycle with reheat of Fig. 8.33, steam leaves the steam generator at 1200 psia and 1200 8 F with a mass flow rate of 50 lbm/s. It leaves the high-pressure turbine at 150 psia and is reheated to 1200 8 F at this pressure. The steam leaves the low-pressure turbine at 6 psia.
Work Problem 8.28 for the following turbine reheat intercept pressure:a) 30 psiab) 90 psia.In the ideal Rankine power cycle with reheat of Fig. 8.33, steam leaves the steam generator at 1200 psia and 1200 8 F with a mass flow rate of 50 lbm/s. It leaves the high-pressure turbine at 150 psia and is
Cogeneration occurs when: (A) The condenser's lost heat is utilized (B) The turbine's large decrease in energy content is used for heating purposes (C) The boiler's heat transfer is used for heating purposes rather than generating electricity (D) The pump creates a larger pressure than needed by
An ideal Rankine cycle with two reheaters is shown in Fig. 8.34. Low pressure is 10 kPa, high pressure is 10 MPa, and the high temperature is 600°C. The first reheater heats 2 MPa steam to 500°C, and the second reheater heats 200 kPa steam to 400°C. For a mass flux of 20 kg/s, show the
An ideal regenerative Rankine cycle with an open feedwater heater is shown in Fig. 8.35. Steam leaves the boiler at 8 MPa and 600 8 C with a mass flow rate of 20 kg/s. It is extracted from the turbine at 1 MPa and sent to the open feedwater heater. The remaining steam leaves the turbine at 20 kPa.
Work Problem 8.31, retaining all quantities except the feedwater heater pressure at state 6 isa) 1200 kPab) 800 kPa.An ideal regenerative Rankine cycle with an open feedwater heater is shown in Fig. 8.35. Steam leaves the boiler at 8 MPa and 600 8 C with a mass flow rate of 20 kg/s. It is extracted
The regenerative Rankine cycle shown in Fig. 8.35 operates with a turbine efficiency of 90% and a mass flow rate of 50 lbm/s. Steam leaves the steam generator at 1200 psia and 1000 8 F. Steam is removed from the turbine at 180 psia and sent to the open feedwater heater. The remaining steam leaves
Work Problem 8.33, retaining all quantities except the preheater intercept pressure which at Section 6 isa) 200 psiab) 160 psia.The regenerative Rankine cycle shown in Fig. 8.35 operates with a turbine efficiency of 90% and a mass flow rate of 50 lbm/s. Steam leaves the steam generator at 1200 psia
An ideal regenerative Rankine cycle contains two open reheaters as shown in the T-s diagram of Fig. 8.36. Steam with a flow rate of 20 kg/s leaves the boiler at 8 MPa and 600°C. Steam is removed from the turbine at 2 MPa and at 400 kPa. The remaining steam leaves the turbine at 20 kPa.
Figure 8.37 shows an ideal Rankine power cycle with regeneration and reheat. Steam leaves the boiler at 8 MPa and 600°C with a mass flow rate of 20 kg/s. Some steam is removed from the high-pressure turbine at 500 kPa and sent to an open feedwater heater. The remaining steam flow leaves the
For the ideal power cycle shown in Fig. 8.37, assume the steam leaving the boiler at state 5 is at 1200 psia and 1000°F with a mass flux of 50 lbm/s. Steam is removed at state 6 at 400 psia and sent to an open feedwater heater. The remaining steam leaves the high-pressure turbine at state 7 at
For the power cycle described in Problem 8.37, determine the cycle efficiency if the pressure at state 6 is 600 psia and at state 7 it is 100 psia.For the ideal power cycle shown in Fig. 8.37, assume the steam leaving the boiler at state 5 is at 1200 psia and 1000°F with a mass flux of 50

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