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engineering
mechanical engineering

Thermodynamics An Engineering Approach 8th edition Yunus A. Cengel, Michael A. Boles - Solutions

Using the equation of state P(v - a) = RT, verify (a) The cyclic relation. (b) The reciprocity relation at constant v.
Based on the generalized charts, the error involved in the enthalpy of CO2 at 300 K and 5 MPa if it is assumed to be an ideal gas is (a) 0% (b) 9% (c) 16% (d) 22% (e) 27%
Based on data from the refrigerant-134a tables, the Joule-Thompson coefficient of refrigerant-134a at 0.8 MPa and 100oC is approximately (a) 0 (b) 25oC/MPa (c) 11oC/MPa (d) 8oC/MPa (e) 26oC/MPa
For a gas whose equation of state is P(v - b) = RT, the specified heat difference cp - cv is equal to (a) R (b) R - b (c) R + b (d) 0 (e) R(1 + v/b)
Derive a relation for the slope of the v = constant lines on a T-P diagram for a gas that obeys the van der Waals equation of state.
Verify the validity of the last Maxwell relation (Eq. 12-19) for refrigerant-134a at 508C and 0.7 MPa.
Reconsider Prob. 12-12. Using EES (or other) software, verify the validity of the last Maxwell relation for refrigerant-134a at the specified state.
Verify the validity of the last Maxwell relation (Eq. 12-19) for steam at 6008F and 275 psia.
Using the Maxwell relations, determine a relation for (∂s/∂P)T for a gas whose equation of state is P(v - b) = RT.
Using the Maxwell relations, determine a relation for (∂s/∂v)T for a gas whose equation of state is (P - a/v2) (v - b) = RT.
Using the Maxwell relations and the ideal-gas equation of state, determine a relation for (∂s/∂v)T for an ideal gas.
Prove that:
Using the Clapeyron equation, estimate the enthalpy of vaporization of refrigerant-134a at 40oC, and compare it to the tabulated value.
Reconsider Prob. 12-21. Using EES (or other) software, plot the enthalpy of vaporization of refrigerant-134a as a function of temperature over the temperature range - 20 to 80oC by using the Clapeyron equation and the refrigerant-134a data in EES. Discuss your results.Prob. 12-21Using the Clapeyron
Using the Clapeyron equation, estimate the enthalpy of vaporization of steam at 300 kPa, and compare it to the tabulated value.
Determine the hfg of refrigerant-134a at 10oF on the basis of (a) The Clapeyron equation. (b) The Clapeyron-Clausius equation. Compare your results to the tabulated hfg value.
0.5-lbm of a saturated vapor is converted to a saturated liquid by being cooled in a weighted piston- cylinder device maintained at 50 psia. During the phase conversion, the system volume decreases by 1.5 ft3; 250 Btu of heat are removed; and the temperature remains fixed at 15oF. Estimate the
Estimate the saturation pressure Psat of the substance in Prob. 12-25E when its temperature is 20oF.Prob. 12-25E0.5-lbm of a saturated vapor is converted to a saturated liquid by being cooled in a weighted piston- cylinder device maintained at 50 psia. During the phase conversion, the system volume
Estimate the sfg of the substance in Problem 12-25E at 15oF.Problem 12-25E0.5-lbm of a saturated vapor is converted to a saturated liquid by being cooled in a weighted piston- cylinder device maintained at 50 psia. During the phase conversion, the system volume decreases by 1.5 ft3; 250 Btu of heat
A table of properties for methyl chloride lists the saturation pressure as 116.7 psia at 100oF. At 100oF, this table also lists hfg = 154.85 Btu/lbm, and vfg = 0.86332 ft3/lbm. Estimate the saturation pressure Psat of methyl chloride at 90oF and 110oF.
Using the Clapeyron-Clausius equation and the triple-point data of water, estimate the sublimation pressure of water at - 30oC and compare to the value in Table A-8.
Show that:
Estimate the volume expansivity b and the isothermal compressibility a of refrigerant-134a at 200 kPa and 30oC.s
Estimate the specific heat difference cp - cv for liquid water at 15 MPa and 80oC.
Determine the change in the internal energy of air, in kJ/kg, as it undergoes a change of state from 100 kPa 20oC to 600 kPa and 300oC using the equation of state P(v - a) = RT where a = 1 m3/kg, and compare the result to the value obtained by using the ideal gas equation of state.
Determine the change in the enthalpy of air, in kJ/ kg, as it undergoes a change of state from 100 kPa and 348C to 800 kPa and 420oC using the equation of state P(v - a) = RT where a = 0.01 m3/kg, and compare the result to the value obtained by using the ideal gas equation of state.
Determine the change in the entropy of air, in kJ/kg?K, as it undergoes a change of state from 100 kPa and 20oC to 600 kPa and 300oC using the equation of state P(v - a) = RT where a = 0.01 m3/kg, and compare the result to the value obtained by using the ideal gas equation of state.
Determine the change in the internal energy of helium, in kJ/kg, as it undergoes a change of state from 100 kPa and 20oC to 600 kPa and 300oC using the equation of state P(v - a) = RT where a = 0.01 m3/kg, and compare the result to the value obtained by using the ideal gas equation of state.
Determine the change in the enthalpy of helium, in kJ/kg, as it undergoes a change of state from 150 kPa and 20oC to 750 kPa and 380oC using the equation of state P(v - a) = RT where a = 0.01 m3/kg, and compare the result to the value obtained by using the ideal gas equation of state.
Determine the change in the entropy of helium, in kJ/kg?K, as it undergoes a change of state from 100 kPa and 20oC to 600 kPa and 300oC using the equation of state P(v - a) = RT where a = 0.01 m3/kg, and compare the result to the value obtained by using the ideal gas equation of state.
Derive expressions for (a) Δu. (b) Δh. (c) Δs for a gas whose equation of state is P(v - a) = RT for an isothermal process.
Derive expressions for (a) Δu. (b) Δh. (c) Δs for a gas that obeys the van der Waals equation of state for an isothermal process.
Derive an expression for the specific heat difference cp - cv for (a) An ideal gas. (b) A van der Waals gas. (c) An incompressible substance.
Show that:
Temperature may alternatively be defined asProve that this definition reduces the net entropy change of two constant-volume systems filled with simple compressible substances to zero as the two systems approach thermal equilibrium.
Derive a relation for the volume expansivity β and the isothermal compressibility α (a) For an ideal gas. (b) For a gas whose equation of state is P(v - a) = RT.
Derive an expression for the isothermal compressibility of a substance whose equation of state iswhere a and b are empirical constants.
Derive an expression for the volume expansivity of a substance whose equation of state iswhere a and b are empirical constants.
Show that β = α(∂P/∂T)v.
Demonstrate that
Consider air at 350 K and 0.75 m3/kg. Using Eq. 12-3,Determine the change in pressure corresponding to an increase of (a) 1 percent in temperature at constant specific volume. (b) 1 percent in specific volume at constant temperature. (c) 1 percent in both the temperature and specific volume.
The Helmholtz function of a substance has the form
Show that the enthalpy of an ideal gas is a function of temperature only and that for an incompressible substance it also depends on pressure.
Describe the inversion line and the maximum inversion temperature.
Estimate the Joule-Thomson coefficient of nitrogen at (a) 120 psia and 350 R. (b) 1200 psia and 700 R. Use nitrogen properties from EES or other source.
Reconsider Prob. 12-57E Using EES (or other) software, plot the Joule-Thomson coefficient for nitrogen over the pressure range 100 to 1500 psia at the enthalpy values 100, 175, and 225 Btu/lbm. Discuss the results. Prob. 12-57E Estimate the Joule-Thomson coefficient of nitrogen at (a) 120 psia and
Steam is throttled slightly from 2 MPa and 500oC. Will the temperature of the steam increase, decrease, or remain the same during this process?
Repeat Problem 12-5 for helium. Problem 12-5 Consider air at 350 K and 0.75 m3/kg. Using Eq. 12-3, determine the change in pressure corresponding to an increase of (a) 1 percent in temperature at constant specific volume. (b) 1 percent in specific volume at constant temperature. (c) 1 percent in
Estimate the Joule-Thomson coefficient of steam at (a) 3 MPa and 300oC. (b) 6 MPa and 500oC.
Estimate the Joule-Thomson-coefficient of refrigerant-134a at 40 psia and 60oF.
Demonstrate that the Joule-Thomson coefficient is given by
Consider a gas whose equation of state is P(v - a) = RT, where a is a positive constant. Is it possible to cool this gas by throttling?
Derive a relation for the Joule-Thomson coefficient and the inversion temperature for a gas whose equation of state is (P + a/v2)v = RT.
Determine the enthalpy of nitrogen, in kJ/kg, at 175 K and 8 MPa using (a) Data from the ideal-gas nitrogen table. (b) The generalized enthalpy departure chart. Compare your results to the actual value of 125.5kJ/kg.
Determine the enthalpy of nitrogen, in Btu/lbm, at 400 R and 2000 psia using (a) Data from the ideal-gas nitrogen table. (b) The generalized enthalpy chart. Compare your results to the actual value of 177.8 Btu/lbm.
Determine the enthalpy change and the entropy change of CO2 per unit mass as it undergoes a change of state from 250 K and 7 MPa to 280 K and 12 MPa, (a) By assuming ideal-gas behavior. (b) By accounting for the deviation from ideal-gas behavior.
Nitrogen gas at 400 K and 300 kPa behaves as an ideal gas. Estimate the cp and cv of the nitrogen at this state, using enthalpy and internal energy data from Table A-18, and compare them to the values listed in Table A-2b.
Saturated water vapor at 400oF is expanded while its pressure is kept constant until its temperature is 800oF. Calculate the change in the specific enthalpy and entropy using (a) The departure charts. (b) The property tables.
Water vapor at 1000 kPa and 600oC is expanded to 500 kPa and 400oC. Calculate the change in the specific entropy and enthalpy of this water vapor using the departure charts and the property tables.
Methane is compressed adiabatically by a steady-flow compressor from 0.8 MPa and - 10oC to 6 MPa and 175oC at a rate of 0.33 kg/s. using the generalized charts, determine the required power input to the compressor.
Reconsider Prob. 12-76. Using EES (or other) software, extend the problem to compare the solutions based on the ideal-gas assumption, generalized chart data, and real fluid data. Also extend the solution to methane.
A 0.05-m3 well-insulated rigid tank contains oxygen at 175 K and 6 MPa. A paddle wheel placed in the tank is turned on, and the temperature of the oxygen rises to 225 K. Using the generalized charts, determine (a) The final pressure in the tank. (b) The paddle-wheel work done during this process.
Nitrogen gas at 800 R and 50 psia behaves as an ideal gas. Estimate the cp and cv of the nitrogen at this state, using enthalpy and internal energy data from Table A-18E, and compare them to the values listed in Table A-2Eb.
Derive relations for (a) Δu. (b) Δh. (c) Δs of a gas that obeys the equation of state (P + a/v2)v = RT for an isothermal process.
Starting with the relation dh = T ds + v dP, show that the slope of a constant-pressure line on an h-s diagram (a) Is constant in the saturation region. (b) Increases with temperature in the superheated region.
Show that
Temperature and pressure may be defined asUsing these definitions, prove that for a simple compressible substance
For ideal gases, the development of the constant-pressure specific heat yieldsProve this by using the definitions of pressure and temperature, T = (ˆ‚u/ˆ‚s)v and P = - (ˆ‚u/ˆ‚v)s.
Starting with mJT = (1/cp)[T(∂v/∂T)p - v] and noting that Pv = ZRT, where Z = Z(P, T) is the compressibility factor, show that the position of the Joule-Thomson coefficient inversion curve on the T-P plane is given by the equation (∂Z/∂T)P = 0.
For a homogeneous (single-phase) simple pure substance, the pressure and temperature are independent properties, and any property can be expressed as a function of these two properties. Taking v = v(P, T), show that the change in specific volume can be expressed in terms of the volume expansivity
Consider an ideal gas at 300 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 305 K and 96 kPa. Estimate the change in the specific volume of the gas using(a) Eq. 12-3(b) The ideal-gas relation at each state.
Argon gas enters a turbine at 1000 psia and 1000 R with a velocity of 300 ft/s and leaves at 150 psia and 500 R with a velocity of 450 ft/s at a rate of 12 lbm/s. Heat is being lost to the surroundings at 75oF at a rate of 80 Btu/s. Using the generalized charts, determine(a) The power output of the
Methane is contained in a piston-cylinder device and is heated at constant pressure of 5 MPa from 100 to 250oC. Determine the heat transfer, work and entropy change per unit mass of the methane using (a) The ideal-gas assumption. (b) The generalized charts. (c) Real fluid data from EES or other
Methane at 50 psia and 1008F is compressed in a steady-flow device to 500 psia and 1100oF. Calculate the change in the specific entropy of the methane and the specific work required for this compression(a) Treating the methane as an ideal gas with temperature variable specific heats.(b) Using the
Determine the second-law efficiency of the compression process described in Prob. 12-98E. Take T0 = 77oF.
Repeat Prob. 13-9 by replacing N2 by O2. In Prob. 13-9 A gas mixture has the following composition on a mole basis: 60 percent N2 and 40 percent CO2. Determine the gravimetric analysis of the mixture, its molar mass, and gas constant.
Using Amagat's law, show thatfor a real-gas mixture of k gases, where Z is the compressibility factor.
An ideal-gas mixture whose apparent molar mass is 20 kg/kmol consists of N2 and three other gases. If the mole fraction of nitrogen is 0.55, its mass fraction is (a) 0.15 (b) 0.23 (c) 0.39 (d) 0.55 (e) 0.77
An ideal-gas mixture consists of 2 kmol of N2 and 6 kmol of CO2. The mass fraction of CO2 in the mixture is (a) 0.175 (b) 0.250 (c) 0.500 (d) 0.750 (e) 0.875
An ideal-gas mixture consists of 2 kmol of N2 and 4 kmol of CO2. The apparent gas constant of the mixture is (a) 0.215kJ/kg∙K (b) 0.225kJ/kg∙K (c) 0.243kJ/kg∙K (d) 0.875kJ/kg∙K (e) 1.24kJ/kg∙K
A rigid tank is divided into two compartments by a partition. One compartment contains 3 kmol of N2 at 400 kPa and the other compartment contains 7 kmol of CO2 at 200 kPa. Now the partition is removed, and the two gases form a homogeneous mixture at 250 kPa. The partial pressure of N2 in the
An 80-L rigid tank contains an ideal-gas mixture of 5 g of N2 and 5 g of CO2 at a specified pressure and temperature. If N2 were separated from the mixture and stored at mixture temperature and pressure, its volume would be (a) 32 L (b) 36 L (c) 40 L (d) 49 L (e) 80 L
An ideal-gas mixture consists of 3 kg of Ar and 6 kg of CO2 gases. The mixture is now heated at constant volume from 250 K to 350 K. The amount of heat transfer is (a) 374 kJ (b) 436 kJ (c) 488 kJ (d) 525 kJ (e) 664 kJ
An ideal-gas mixture consists of 60 percent helium and 40 percent argon gases by mass. The mixture is now expanded isentropically in a turbine from 400oC and 1.2 MPa to a pressure of 200 kPa. The mixture temperature at turbine exit is (a) 56oC (b) 195oC (c) 130oC (d) 112oC (e) 400oC
One compartment of an insulated rigid tank contains 2 kmol of CO2 at 20oC and 150 kPa while the other compartment contains 5 kmol of H2 gas at 35oC and 300 kPa. Now the partition between the two gases is removed, and the two gases form a homogeneous ideal-gas mixture. The temperature of the mixture
A piston-cylinder device contains an ideal-gas mixture of 3 kmol of He gas and 7 kmol of Ar gas at 50oC and 400 kPa. Now the gas expands at constant pressure until its volume doubles. The amount of heat transfer to the gas mixture is (a) 6.2 MJ (b) 4.2 MJ (c) 27 MJ (d) 10 MJ (e) 67 MJ
A gas mixture consists of 2 kg of O2, 5 kg of N2, and 7 kg of CO2. Determine (a) The mass fraction of each component. (b) The mole fraction of each component. (c) The average molar mass and gas constant of the mixture.
An ideal-gas mixture of helium and argon gases with identical mass fractions enters a turbine at 1500 K and 1 MPa at a rate of 0.12 kg/s, and expands isentropically to 100 kPa. The power output of the turbine is (a) 253 kW (b) 310 kW (c) 341 kW (d) 463 kW (e) 550 kW
Determine the mole fractions of a gas mixture that consists of 75 percent CH4 and 25 percent CO2 by mass. Also, determine the gas constant of the mixture.
A gas mixture consists of 6 kmol of H2 and 2 kmol of N2. Determine the mass of each gas and the apparent gas constant of the mixture.
Express Dalton's law of additive pressures. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?
Express Amagat's law of additive volumes. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?
How is the P-v-T behavior of a component in an ideal-gas mixture expressed? How is the P-v-T behavior of a component in a real-gas mixture expressed?
What is the difference between the component pressure and the partial pressure? When are these two equivalent?
What is the difference between the component volume and the partial volume? When are these two equivalent?
Atmospheric contaminants are often measured in parts per million (by volume). What would the partial pressure of refrigerant-134a be in atmospheric air at 100 kPa and 20oC to form a 100-ppm contaminant?
A mixture of gases consists of 30 percent hydrogen, 40 percent helium, and 30 percent nitrogen by volume. Calculate the mass fractions and apparent molecular weight of this mixture.
A gas mixture at 600 R and 20 psia consists of 1 lbm of CO2 and 3 lbm of CH4. Determine the partial pressure of each gas and the apparent molar mass of the gas mixture.
A gas mixture at 350 K and 300 kPa has the following volumetric analysis: 65 percent N2, 20 percent O2, and 15 percent CO2. Determine the mass fraction and partial pressure of each gas.
In an ideal gas mixture the partial pressures of the component gases are as follows: CO2, 20 kPa; O2, 30 kPa; and N2, 50 kPa. Determine the mole fractions and mass fractions of each component. Calculate the apparent molar mass, the apparent gas constant, the constant-volume specific heat, and the

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