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engineering
mechanical engineering
Thermodynamics An Engineering Approach 8th edition Yunus A. Cengel, Michael A. Boles - Solutions
A mixture of 3 mol of CO2 and 3 mol of O2 is heated to 3400 K at a pressure of 2 atm. Determine the equilibrium composition of the mixture, assuming that only CO2, CO, O2, and O are present.
Reconsider Prob. 16–85. Using EES (or other) software, study the effect of pressure on the equilibrium composition by varying pressure from 1 atm to 10 atm. Plot the amount of CO present at equilibrium as a function of pressure.
Estimate the enthalpy of reaction hR for the combustion process of hydrogen at 2400 K, using (a) Enthalpy data and (b) KP data.
Reconsider Prob. 16–87. Using EES (or other) software, investigate the effect of temperature on the enthalpy of reaction using both methods by varying the temperature from 2000 to 3000 K.
Using the enthalpy of reaction data and the KP value at 2800 K, estimate the KP value of the dissociation process O2 2O at 3000 K.
Show that when the three phases of a pure substance are in equilibrium, the specific Gibbs function of each phase is the same.
Show that when the two phases of a two-component system are in equilibrium, the specific Gibbs function of each phase of each component is the same.
A constant-volume tank initially contains 1 kmol of carbon monoxide CO and 3 kmol of oxygen O2 (no nitrogen) at 25°C and 2 atm. Now the mixture is ignited and the CO burns completely to carbon dioxide CO2. If the final temperature in the tank is 500 K, determine the final pressure in the tank and
Using Henry’s law, show that the dissolved gases in a liquid can be driven off by heating the liquid
Consider a glass of water in a room at 25°C and 100 kPa. If the relative humidity in the room is 70 percent and the water and the air are in thermal equilibrium, determine (a) The mole fraction of the water vapor in the room air, (b) The mole fraction of the water vapor in the air adjacent to
Repeat Prob. 16–94 for a relative humidity of 25 percent.
A carbonated drink is fully charged with CO2 gas at 17°C and 600 kPa such that the entire bulk of the drink is in thermodynamic equilibrium with the CO2–water vapor mixture. Now consider a 2-L soda bottle. If the CO2 gas in that bottle were to be released and stored in a container at 20°C and
Ethyl alcohol (C2H5OH(g)) at 25°C is burned in a steady-flow adiabatic combustion chamber with 40 percent excess air that also enters at 25°C. Determine the adiabatic flame temperature of the products at 1 atm assuming the only significant equilibrium reaction is CO2 = CO + O2. Plot the adiabatic
Tabulate the natural log of the equilibrium constant as a function of temperature between 298 to 3000 K for the equilibrium reaction CO + H2O = CO2 + H2. Compare your results to those obtained by combining the ln KP values for the two equilibrium reactions CO2 = CO + 1/2 and H2O = H2 + O2 given in
It is desired to control the amount of CO in the products of combustion of octane C8H18 so that the volume fraction of CO in the products is less than 0.1 percent. Determine the percent theoretical air required for the combustion of octane at 5 atm such that the reactant and product temperatures
If the equilibrium constant for the reaction H2 + 1/2O2 H→2O is K, the equilibrium constant for the reaction 2H2O → 2H2 + O2 at the same temperature is (a) 1/K (b) 1/(2K) (c) 2K (d) K2 (e) 1/K2
If the equilibrium constant for the reaction CO + 1/2O2→CO2 is K, the equilibrium constant for the reaction Co2 + 3n2 → co + 1/2o2 +3N2 at the same temperature is (a) 1/K (b) 1/(K + 3) (c) 4K (d) K (e) 1/K2
The equilibrium constant for the reaction H2 + at 1 atm and 1500°C is given to be K. Of the reactions given below, all at 1500°C, the reaction that has a different equilibrium constant is (a) H2 + 12O2 → H2O at 5 atm (b) 2H2 + O2 → 2H2O at 1 atm (c) H2 + O2 → H2O +
Of the reactions given below, the reaction whose equilibrium composition at a specified temperature is not affected by pressure is (a) H2 + 1/2O2 →H2O (b) CO + 1/2O2 → CO2 (c) N2 + O2 → 2NO (d) N2 → 2N (e) All of the above.
Of the reactions given below, the reaction whose number of moles of products increases by the addition of inert gases into the reaction chamber at constant pressure and temperature is (a) H2 + 1/2O2 → H2O (b) CO+ 1/2O2 → CO2 (c) N2 + O2 → 2NO (d) N2 → 2N (e) All of the
Moist air is heated to a very high temperature. If the equilibrium composition consists of H2O, O2, N2, OH, H2, and NO, the number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is (a) 1 (b) 2 (c) 3 (d) 4 (e) 5
Propane C3H8 is burned with air, and the combustion products consist of CO2, CO, H2O, O2, N2, OH, H2, and NO. The number of equilibrium constant relations needed to determine the equilibrium composition of the mixture is (a) 1 (b) 2 (c) 3 (d) 4 (e) 5
Consider a gas mixture that consists of three components. The number of independent variables that need to be specified to fix the state of the mixture is (a) 1 (b) 2 (c) 3 (d) 4 (e) 5
The value of Henry’s constant for CO2 gas dissolved in water at 290 K is 12.8 MPa. Consider water exposed to atmospheric air at 100 kPa that contains 3 percent CO2 by volume. Under phase equilibrium conditions, the mole fraction of CO2 gas dissolved in water at 290 K is (a) 2.3 x 10-4 (b) 3.0 x
The solubility of nitrogen gas in rubber at 25°C is 0.00156 kmol/m3 • bar. When phase equilibrium is established, the density of nitrogen in a rubber piece placed in a nitrogen gas chamber at 800 kPa is (a) 0.012 kg/m3 (b) 0.35 kg/m3 (c) 0.42 kg/m3 (d) 0.56 kg/m3 (e) 0.078 kg/m3
How and why is the stagnation enthalpy h0 defined? How does it differ from ordinary (static) enthalpy?
In air-conditioning applications, the temperature of air is measured by inserting a probe into the flow stream. Thus, the probe actually measures the stagnation temperature. Does this cause any significant error?
Determine the stagnation temperature and stagnation pressure of air that is flowing at 44 kPa, 245.9 K, and 470 m/s.
Air at 300 K is flowing in a duct at a velocity of (a) 1, (b) 10, (c) 100, and (d) 1000 m/s Determine the temperature that a stationary probe inserted into the duct will read for each case.
Calculate the stagnation temperature and pressure for the following substances flowing through a duct: (a) Helium at 0.25 MPa, 50°C, and 240 m/s (b) Nitrogen at 0.15 MPa, 0°C, and 300 m/s; and (c) Steam at 0.1 MPa, 350°C, and 480 m/s
Air enters a compressor with a stagnation pressure of 100 kPa and a stagnation temperature of 27°C, and it is compressed to a stagnation pressure of 900 kPa. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of 0.02 kg/s.
Steam flows through a device with a stagnation pressure of 120 psia, a stagnation temperature of 700°F, and a velocity of 900 ft/s. Assuming ideal-gas behavior, determine the static pressure and temperature of the steam at this state.
Products of combustion enter a gas turbine with a stagnation pressure of 1.0 MPa and a stagnation temperature of 750°C, and they expand to a stagnation pressure of 100 kPa. Taking k = 1.33 and R = 0.287 kJ/kg • K for the products of combustion, and assuming the expansion process to be
Air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is 400°C, and the velocity is 570 m/s. Determine the static pressure and temperature of the air at this state.
What is sound? How is it generated? How does it travel? Can sound waves travel in a vacuum?
Is it realistic to assume that the propagation of sound waves is an isentropic process? Explain.
Is the sonic velocity in a specified medium a fixed quantity, or does it change as the properties of the medium change? Explain.
In which medium will sound travel fastest for a given temperature: air, helium, or argon?
In which medium does a sound wave travel faster: in air at 20°C and 1 atm or in air at 20°C and 5 atm?
Does the Mach number of a gas flowing at a constant velocity remain constant? Explain.
Determine the speed of sound in air at (a) 300 K and (b) 1000 K. Also determine the Mach number of an aircraft moving in air at a velocity of 280 m/s for both cases.
Carbon dioxide enters an adiabatic nozzle at 1200 K with a velocity of 50 m/s and leaves at 400 K. Assuming constant specific heats at room temperature, determine the Mach number (a) at the inlet and (b) at the exit of the nozzle. Assess the accuracy of the constant specific heat assumption.
Nitrogen enters a steady-flow heat exchanger at 150 kPa, 10°C, and 100 m/s, and it receives heat in the amount of 120 kJ/kg as it flows through it. Nitrogen leaves the heat exchanger at 100 kPa with a velocity of 200 m/s. Determine the Mach number of the nitrogen at the inlet and the exit of the
Assuming ideal-gas behavior, determine the speed of sound in refrigerant-134a at 0.1 MPa and 60°C.
The Airbus A-340 passenger plane has a maximum takeoff weight of about 260,000 kg, a length of 64 m, a wing span of 60 m, a maximum cruising speed of 945 km/h, a seating capacity of 271 passengers, maximum cruising altitude of 14,000 m, and a maximum range of 12,000 km. The air temperature at the
Steam flows through a device with a pressure of 120 psia, a temperature of 700°F, and a velocity of 900 ft/s. Determine the Mach number of the steam at this state by assuming ideal-gas behavior with k = 1.
Reconsider Prob. 17–24E Using EES (or other) software, compare the Mach number of steam flow over the temperature range 350 to 700°F. Plot the Mach number as a function of temperature.
The isentropic process for an ideal gas is expressed as Pv k = constant. Using this process equation and the definition of the speed of sound (Eq. 17–9), obtain the expression for the speed of sound for an ideal gas (Eq. 17–11).
Air expands isentropically from 1.5 MPa and 60°C to 0.4 MPa. Calculate the ratio of the initial to final speed of sound.
Repeat Prob. 17–27 for helium gas.
Air expands isentropically from 170 psia and 200°F to 60 psia. Calculate the ratio of the initial to final speed of sound.
Consider a converging nozzle with sonic velocity at the exit plane. Now the nozzle exit area is reduced while the nozzle inlet conditions are maintained constant. What will happen to? (a) The exit velocity and (b) The mass flow rate through the nozzle?
A gas initially at a supersonic velocity enters an adiabatic converging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.
A gas initially at a supersonic velocity enters an adiabatic diverging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.
A gas initially at a supersonic velocity enters an adiabatic converging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.
A gas initially at a subsonic velocity enters an adiabatic diverging duct. Discuss how this affects (a) the velocity, (b) the temperature, (c) the pressure, and (d) the density of the fluid.
Air enters a converging–diverging nozzle at a pressure of 1.2 MPa with negligible velocity. What is the lowest pressure that can be obtained at the throat of the nozzle?
Helium enters a converging–diverging nozzle at 0.7 MPa, 800 K, and 100 m/s. What are the lowest temperature and pressure that can be obtained at the throat of the nozzle?
Calculate the critical temperature, pressure, and density of (a) Air at 200 kPa, 100°C, and 250 m/s, and (b) Helium at 200 kPa, 40°C, and 300 m/s.
Quiescent carbon dioxide at 600 kPa and 400 K is accelerated isentropically to a Mach number of 0.5. Determine the temperature and pressure of the carbon dioxide after acceleration.
Air at 200 kPa, 100°C, and Mach number Ma = 0.8 flows through a duct. Find the velocity and the stagnation pressure, temperature, and density of the air.
Reconsider Prob. 17–41. Using EES (or other) software, study the effect of Mach numbers in the range 0.1 to 2 on the velocity, stagnation pressure, temperature, and density of air. Plot each parameter as a function of the Mach number.
Air at 30 psia, 212°F, and Mach number Ma = 0.8 flows through a duct. Calculate the velocity and the stagnation pressure, temperature, and density of air.
An aircraft is designed to cruise at Mach number Ma = 1.2 at 8000 m where the atmospheric temperature is 236.15 K. Determine the stagnation temperature on the leading edge of the wing.
Consider subsonic flow in a converging nozzle with fixed inlet conditions. What is the effect of dropping the back pressure to the critical pressure on? (a) The exit velocity, (b) The exit pressure, and (c) The mass flow rate through the nozzle?
Consider gas flow through a converging nozzle with specified inlet conditions. We know that the highest velocity the fluid can have at the nozzle exit is the sonic velocity, at which point the mass flow rate through the nozzle is a maximum. If it were possible to achieve hypersonic velocities at
How does the parameter Ma* differ from the Mach number Ma?
Explain why the maximum flow rate per unit area for a given gas depends only on Po/√To. For and ideal gas with K = 1.4 and R = 0.287 kJ/kg. K, find the constant a such that m/A* = a Po/√To.
For an ideal gas obtain an expression for the ratio of the velocity of sound where Ma = 1 to the speed of sound based on the stagnation temperature, c*/c0.
An ideal gas flows through a passage that first converges and then diverges during an adiabatic, reversible, steady-flow process. For subsonic flow at the inlet, sketch the variation of pressure, velocity, and Mach number along the length of the nozzle when the Mach number at the minimum flow area
Repeat Prob. 17–56 for supersonic flow at the inlet.
Air enters a nozzle at 0.2 MPa, 350 K, and a velocity of 150 m/s. Assuming isentropic flow, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?
Repeat Prob. 17–58 assuming the entrance velocity is negligible.
Air enters a nozzle at 30 psia, 630 R, and a velocity of 450 ft/s. Assuming isentropic flow, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?
Air enters a converging–diverging nozzle at 0.5 MPa with a negligible velocity. Assuming the flow to be isentropic, determine the back pressure that will result in an exit Mach number of 1.8
Nitrogen enters a converging–diverging nozzle at 700 kPa and 450 K with a negligible velocity. Determine the critical velocity, pressure, temperature, and density in the nozzle.
An ideal gas with k = 1.4 is flowing through a nozzle such that the Mach number is 2.4 where the flow area is 25 cm2. Assuming the flow to be isentropic, determine the flow area at the location where the Mach number is 1.2.
Repeat Prob. 17–63 for an ideal gas with k = 1.33.
Air at 900 kPa and 400 K enters a converging nozzle with a negligible velocity. The throat area of the nozzle is 10 cm2. Assuming isentropic flow, calculate and plot the exit pressure, the exit velocity, and the mass flow rate versus the back pressure Pb for 0.9 > Pb > 0.1 MPa.
Reconsider Prob. 17–65. Using EES (or other) software, solve the problem for the inlet conditions of 1 MPa and 1000 K.
Air enters a converging–diverging nozzle of a supersonic wind tunnel at 150 psia and 100°F with a low velocity. The flow area of the test section is equal to the exit area of the nozzle, which is 5 ft2. Calculate the pressure, temperature, velocity, and mass flow rate in the test section for a
Can a shock wave develop in the converging section of a converging–diverging nozzle? Explain.
What do the states on the Fan no line and the Rayleigh line represent? What do the intersection points of these two curves represent?
How do oblique shocks occur? How do oblique shocks differ from normal shocks?
For an oblique shock to occur, does the upstream flow have to be supersonic? Does the flow downstream of an oblique shock have to be subsonic?
It is claimed that an oblique shock can be analyzed like a normal shock provided that the normal component of velocity (normal to the shock surface) is used in the analysis. Do you agree with this claim?
Consider supersonic airflow approaching the nose of a two-dimensional wedge and experiencing an oblique shock. Under what conditions does an oblique shock detach from the nose of the wedge and form a bow wave? What is the numerical value of the shock angle of the detached shock at the nose?
Consider supersonic flow impinging on the rounded nose of an aircraft. Will the oblique shock that forms in front of the nose be an attached or detached shock? Explain.
Are the isentropic relations of ideal gases applicable for flows across? (a) Normal shock waves, (b) Oblique shock waves, and (c) Prandtl–Meyer expansion waves?
For an ideal gas flowing through a normal shock, develop a relation for V2/V1 in terms of k, Ma1, and Ma2.
Air enters a converging–diverging nozzle of a supersonic wind tunnel at 1.5 MPa and 350 K with a low velocity. If a normal shock wave occurs at the exit plane of the nozzle at Ma = 2, determine the pressure, temperature, Mach number, velocity, and stagnation pressure after the shock wave.
Air enters a converging–diverging nozzle with low velocity at 2.0 MPa and 100°C. If the exit area of the nozzle is 3.5 times the throat area, what must the back pressure be to produce a normal shock at the exit plane of the nozzle?
What must the back pressure be in Prob. 17–80 for a normal shock to occur at a location where the cross-sectional area is twice the throat area?
Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.5. If the pressure and temperature of air are 61.64 kPa and 262.15 K, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the
Calculate the entropy change of air across the normal shock wave in Prob. 17–82.
Air flowing steadily in a nozzle experiences a normal shock at a Mach number of Ma = 2.5. If the pressure and temperature of air are 10.0 psia and 440.5 R, respectively, upstream of the shock, calculate the pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the
Reconsider Prob. 17–84E Using EES (or other) software, study the effects of both air and helium flowing steadily in a nozzle when there is a normal shock at a Mach number in the range 2 < Ma1 < 3.5. In addition to the required information, calculate the entropy change of the air and helium across
Air enters a normal shock at 22.6 kPa, 217 K, and 680 m/s. Calculate the stagnation pressure and Mach number upstream of the shock, as well as pressure, temperature, velocity, Mach number, and stagnation pressure downstream of the shock.
Calculate the entropy change of air across the normal shock wave in Prob. 17–86.
Using EES (or other) software, calculate and plot the entropy change of air across the normal shock for upstream Mach numbers between 0.5 and 1.5 in increments of 0.1. Explain why normal shock waves can occur only for upstream Mach numbers greater than Ma = 1.
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