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engineering
mechanical engineering

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

An ideal gas refrigeration cycle using air as the working fluid operates between the pressure limits of 80 and 280 kPa. Air is cooled to 35°C before entering the turbine. The lowest temperature of this cycle is (a) -58°C (b) -26°C (c) 5°C (d) 11°C (e) 24°C
Consider an ideal gas refrigeration cycle using helium as the working fluid. Helium enters the compressor at 100 kPa and -10°C and compressed to 250 kPa. Helium is then cooled to 20°C before it enters the turbine. For a mass flow rate of 0.2 kg/s, the net power input required is (a) 9.3 kW (b)
An absorption air-conditioning system is to remove heat from the conditioned space at 20°C at a rate of 150 kJ/s while operating in an environment at 35°C heat is to be supplied from a geothermal source at 140°C. The minimum rate of heat supply is (a) 86 kJ/s (b) 21 kJ/s (c) 30 kJ/s (d) 61
Consider a refrigerator that operates on the vapor compression refrigeration cycle with R-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 160 kPa, and exits at 800 kPa and 50°C, and leaves the condenser as saturated liquid at 800 kPa. The coefficient of
Consider the function z(x, y). Plot a differential surface on x-y-z coordinates and indicate ∂x, dx, ∂y, dy, (∂z) x, (∂z)y and dz.
What is the difference between partial differentials and ordinary differentials?
Consider the function z(x, y), its partial derivatives (∂z/∂x)y and (∂z/∂y)x, and the total derivative dz/dx. (a) How do the magnitudes (∂x)y and dx compare? (b) How do the magnitudes (∂z)y and dz compare? (c) Is there any relation among dz, (∂z)x, and
Consider air at 400 K and 0.90 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, and (c) 1 percent in both the temperature and specific
Repeat Problem 12–8 for helium.
Prove for an ideal gas that (a) The P = constant lines on a T-v diagram are straight lines and (b) The high-pressure lines are steeper than the low-pressure lines.
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.
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.
Nitrogen gas at 600 R and 30 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.
Consider an ideal gas at 400 K and 100 kPa. As a result of some disturbance, the conditions of the gas change to 404 K and 96 kPa. Estimate the change in the specific volume of the gas using (a) Eq. 12–3 and (b) The ideal-gas relation at each state.
Using the equation of state P(v - a) = RT, verify (a) The cyclic relation and (b) The reciprocity relation at constant v.
Verify the validity of the last Maxwell relation (Eq. 12–19) for refrigerant-134a at 80°C and 1.2 MPa.
Reconsider Prob. 12–16. 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 800°F and 400 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.
What is the value of the Clapeyron equation in thermodynamics?
Using the Clapeyron equation, estimate the enthalpy of vaporization of refrigerant-134a at 40°C, and compare it to the tabulated value.
Reconsider Prob. 12–25. Using EES (or other) software, plot the enthalpy of vaporization of refrigerant-134a as a function of temperature over the temperature range -20 to 80°C by using the Clapeyron equation and the refrigerant-134a data in EES. Discuss your results.
Using the Clapeyron equation, estimate the enthalpy of vaporization of steam at 300 kPa, and compare it to the tabulated value.
Calculate the hfg and sfg of steam at 120°C from the Clapeyron equation, and compare them to the tabulated values.
Determine the hfg of refrigerant-134a at 50°F on the basis of (a) The Clapeyron equation and (b) The Clapeyron-Clausius equation. Compare your results to the tabulated hfg value.
Plot the enthalpy of vaporization of steam as a function of temperature over the temperature range 10 to 200°C by using the Clapeyron equation and steam data in EES.
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 value in Table A–8.
Can the variation of specific heat cp with pressure at a given temperature be determined from a knowledge of Pv- T data alone?
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.
Derive expressions for (a) ∆u, (b) ∆h, and (c) ∆s for a gas that obeys the van der Waals equation of state for an isothermal process.
Derive expressions for (a) ∆u, (b) ∆h, and (c) ∆s for a gas whose equation of state is P(v - a) = RT for an isothermal process.
Derive expressions for (∂u/∂P) T and (∂h/∂v)T in terms of P, v, and T only.
Derive an expression for the specific-heat difference cp - cv for (a) An ideal gas, (b) A van der Waals gas, and (c) An incompressible substance.
Estimate the specific-heat difference cp - cv for liquid water at 15 MPa and 80°C.
Estimate the specific-heat difference cp - cv for liquid water at 1000 psia and 150°F.
Derive a relation for the volume expansively b and the isothermal compressibility a (a) For an ideal gas and (b) For a gas whose equation of state is P (v - a) = RT.
Estimate the volume expansively b and the isothermal compressibility a of refrigerant-134a at 200 kPa and 30°C.
Describe the inversion line and the maximum inversion temperature.
Will the temperature of helium change if it is throttled adiabatically from 300 K and 600 kPa to 150 kPa?
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.
Estimate the Joule-Thomson coefficient of steam at (a) 3 MPa and 300°C and (b) 6 MPa and 500°C.
Estimate the Joule-Thomson coefficient of nitrogen at (a) 200 psia and 500 R and (b) 2000 psia and 400 R. Use nitrogen properties from EES or other source.
Reconsider Prob 12–50E 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.
Estimate the Joule-Thomson coefficient of refrigerant- 134a at 0.7 MPa and 50°C.
Steam is throttled slightly from 1 MPa and 300°C. Will the temperature of the steam increase, decrease, or remain the same during this process?
On the generalized enthalpy departure chart, the normalized enthalpy departure values seem to approach zero as the reduced pressure PR approaches zero. How do you explain this behavior?
Determine the enthalpy of nitrogen, in kJ/kg, at 175 K and 8 MPa using (a) Data from the ideal-gas nitrogen table and (b) The generalized enthalpy departure chart. Compare your results to the actual value of 125.5 kJ/kg.
Determine the enthalpy of nitrogen, in Btu/lbm, at 400 R and 2000 psia using (a) Data from the ideal-gas nitrogen table and (b) The generalized enthalpy chart. Compare your results to the actual value of 177.8 Btu/lbm.
What is the error involved in the (a) Enthalpy and (b) Internal energy of CO2 at 350 K and 10 MPa if it is assumed to be an ideal gas?
Determine the enthalpy change and the entropy change of nitrogen per unit mole as it undergoes a change of state from 225 K and 6 MPa to 320 K and 12 MPa, (a) By assuming ideal-gas behavior and (b) By accounting for the deviation from ideal-gas behavior through the use of generalized charts.
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 and (b) By accounting for the deviation from ideal-gas behavior.
Methane is compressed adiabatically by a steady-flow compressor from 2 MPa and -10°C to 10 MPa and 110°C at a rate of 0.55 kg/s. Using the generalized charts, determine the required power input to the compressor.
Propane is compressed isothermally by a piston– cylinder device from 100°C and 1 MPa to 4 MPa. Using the generalized charts, determine the work done and the heat transfer per unit mass of propane.
Reconsider Prob. 12–63. 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.
Propane is compressed isothermally by a piston– cylinder device from 200°F and 200 psia to 800 psia. Using the generalized charts, determine the work done and the heat transfer per unit mass of the propane.
Determine the energy destruction associated with the process described in Prob. 12–63. Assume T0 = 30°C.
Carbon dioxide enters an adiabatic nozzle at 8 MPa and 450 K with a low velocity and leaves at 2 MPa and 350 K. Using the generalized enthalpy departure chart, determine the exit velocity of the carbon dioxide.
Reconsider Prob. 12–67. Using EES (or other) software, compare the exit velocity to the nozzle assuming ideal-gas behavior, the generalized chart data, and EES data for carbon dioxide.
A 0.08-m3 well-insulated rigid tank contains oxygen at 220 K and 10 MPa. A paddle wheel placed in the tank is turned on, and the temperature of the oxygen rises to 250 K. Using the generalized charts, determine (a) The final pressure in the tank and (b) The paddle-wheel work done during this
Carbon dioxide is contained in a constant-volume tank and is heated from 100°C and 1 MPa to 8 MPa. Determine the heat transfer and entropy change per unit mass of the carbon dioxide using (a) The ideal-gas assumption, (b) The generalized charts, and (c) Real fluid data from EES or other
For B > 0, prove that at every point of a single-phase region of an h-s diagram, the slope of a constant pressure (P = constant) line is greater than the slope of a constant-temperature (T = constant) line, but less than the slope of a constant-volume (v = constant) line.
Using the cyclic relation and the first Maxwell relation, derive the other three Maxwell relations.
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 and (b) Increases with temperature in the superheated region.
Derive relations for (a) ∆u, (b) ∆h, and (c) ∆s of a gas that obeys the equation of state (P + a/v 2)v = RT for an isothermal process.
Show That
Estimate the cp of nitrogen at 300 kPa and 400 K, using (a) The relation in the above problem and (b) Its definition. Compare your results to the value listed in Table A–2b.
Steam is throttled from 4.5 MPa and 300°C to 2.5 MPa. Estimate the temperature change of the steam during this process and the average Joule-Thomson coefficient.
A rigid tank contains 1.2 m3 of argon at -100°C and 1 MPa. Heat is now transferred to argon until the temperature in the tank rises to 0°C. Using the generalized charts, determine (a) The mass of the argon in the tank, (b) The final pressure, and (c) The heat transfer.
Argon gas enters a turbine at 7 MPa and 600 K with a velocity of 100 m/s and leaves at 1 MPa and 280 K with a velocity of 150 m/s at a rate of 5 kg/s. Heat is being lost to the surroundings at 25°C at a rate of 60 kW. Using the generalized charts, determine(a) The power output of the turbine
Reconsider Prob. 12–79. Using EES (or other) software, solve the problem assuming steam is the working fluid by using the generalized chart method and EES data for steam. Plot the power output and the energy destruction rate for these two calculation methods against the turbine exit pressure as
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 75°F at a rate of 80 Btu/s. Using the generalized charts, determine (a) The power output of
An adiabatic 0.2-m3 storage tank that is initially evacuated is connected to a supply line that carries nitrogen at 225 K and 10 MPa. A valve is opened, and nitrogen flows into the tank from the supply line. The valve is closed when the pressure in the tank reaches 10 MPa. Determine the final
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 expansively
Repeat Prob. 12–83 for an isobaric process.
The volume expansivity of water at 20°C is b = 0.207 x 10-6 K-1. Treating this value as a constant, determine the change in volume of 1 m3 of water as it is heated from 10°C to 30°C at constant pressure.
The volume expansivity b values of copper at 300 K and 500 K are 49.2 x 10-6 K-1 and 54.2 x 10-6 K-1, respectively, and b varies almost linearly in this temperature range. Determine the percent change in the volume of a copper block as it is heated from 300 K to 500 K at atmospheric pressure.
Starting with μπ = (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.
Consider an infinitesimal reversible adiabatic compression or expansion process. By taking s = s(P, v) and using the Maxwell relations, show that for this process Pvk = constant, where k is the isentropic expansion exponent defined as k = v/P (∂P/∂) Also, show that the isentropic
Refrigerant-134a undergoes an isothermal process at 60°C from 3 to 0.1 MPa in a closed system. Determine the work done by the refrigerant-134a by using the tabular (EES) data and the generalized charts, in kJ/kg.
Methane is contained in a piston–cylinder device and is heated at constant pressure of 4 MPa from 100 to 350°C. Determine the heat transfer, work and entropy change per unit mass of the methane using (a) The ideal-gas assumption, (b) The generalized charts, and (c) Real fluid data from EES
A substance whose Joule-Thomson coefficient is negative is throttled to a lower pressure. During this process, (select the correct statement) (a) The temperature of the substance will increase. (b) The temperature of the substance will decrease. (c) The entropy of the substance will remain
Consider the liquid–vapor saturation curve of a pure substance on the P-T diagram. The magnitude of the slope of the tangent line to this curve at a temperature T (in Kelvin) is (a) Proportional to the enthalpy of vaporization hfg at that temperature. (b) Proportional to the temperature T. (c)
Based on the generalized charts, the error involved in the enthalpy of CO2 at 350 K and 8 MPa if it is assumed to be an ideal gas is (a) 0 (b) 20% (c) 35% (d) 26% (e) 65%
Based on data from the refrigerant-134a tables, the Joule-Thompson coefficient of refrigerant-134a at 0.8 MPa and 100°C is approximately (a) 0 (b) -5°C/MPa (c) 11°C/MPa (d) 8°C/MPa (e) 26°C/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)
What are mass and mole fractions?
Using the definitions of mass and mole fractions derive a relation between them.
Consider a mixture of two gases A and B. Show that when the mass fractions mfA and mfB are known, the mole fractions can be determined from where MA and MB are the molar masses of A and B.
The composition of moist air is given on a molar basis to be 78 percent N2, 20 percent O2, and 2 percent water vapor. Determine the mass fractions of the constituents of air.
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.
Repeat Prob. 13–11 by replacing N2 by O2.
A gas mixture consists of 5 kg of O2, 8 kg of N2, and 10 kg of CO2. Determine (a) The mass fraction of each component, (b) The mole fraction of each component, and (c) The average molar mass and gas constant of the mixture.
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 8 kmol of H2 and 2 kmol of N2. Determine the mass of each gas and the apparent gas constant of the mixture. Answers: 16 kg, 56 kg, 1.155 kJ/kg • K
A gas mixture consists of 5 lb mol of H2 and 4 lb mol of N2. Determine the mass of each gas and the apparent gas constant of the mixture.
A gas mixture consists of 20 percent O2, 30 percent N2, and 50 percent CO2 on mass basis. Determine the volumetric analysis of the mixture and the apparent gas constant.
Is a mixture of ideal gases also an ideal gas? Give an example.

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