Questions and Answers of Thermodynamics Fundamentals

In analogy with the way the Gibbs and Helmholtz energy are obtained by considering processes occurring in a closed system, obtain the thermodynamic function that most simply allows for the
Work out the differential relation between specific entropy of a simple compressible fluid and its temperature and pressure, such that it can be evaluated with the help of cP and an equation of state
How can the residual part of cP of a simple compressible fluid be evaluated from an an equation of state in the form P = P - (T, v)?
Obtain the expression for the isothermal compressibility κ from the Helmholtz energy a = a - (T,v).
Assume that the equation of state for a certain fluid is given as g = g - (T,P) (for example, this is the case for the IF97 equation of state, but it has also been applied for mixture equations of
Suppose we want to store 100 kg of carbon dioxide in a 0.5 m3 tank at 320 K and we want to calculate the required pressure using different thermodynamic models. Given that the critical temperature
Given the speed of sound values for ethane from A. F. Estrada-Alexanders and J. P. M. Trusler, ?The speed of sound and derived thermodynamic properties of ethane at temperatures between 220 K and 450
The vapor pressure of refrigerant R134a can be approximated with the Antoine equation ?with P in kPa and T in K, A = 14.41 kPa, B = 2094 kPa ? K, and C = ?33.06 K. The critical temperature is Tc?=
Propane is to be stored at 4 MPa, 100°C. The critical temperature and pressure of propane are equal to 369.8 K and 4.23 MPa, respectively. Estimate the specific volume at these conditions. How large
Compare the specific volume of steam at 40 MPa, 800 K as obtained with the ideal gas equation of state, the generalized compressibility chart, and the IF97 model. The critical temperature and
Calculate the vapor pressure of water at 150°C using the van der Waals equation of state. Repeat the calculation at 370°C. How do these values compare with values obtained with the IF97 model?
What is the relation between the isothermal compressibility and the speed of sound for a simple compressible fluid?
The Joule?Thomson (or Joule?Kelvin) coefficient for a simple compressible substance is defined as (a) Prove that (b) Discuss how this equation might be used;(c) Show that the Joule?Thomson
Obtain equations for the speed of sound and isothermal, isobaric, and isentropic compressibility a valid for the van der Waals equation of state.
Evaluate the specific volume of heptane for Tr = 1.1 and Pr = 3.5 using(a) The van der Waals equation of state (Tc = 540.13 K, Pc?= 27.36 bar);(b) The generalized compressibility chart of Figure
Obtain charts like those of Figure 6.23 in order to compare values for propane calculated with STANMIX and TPSI. What can you infer from these charts about the accuracy of the cubic equation of state
Estimate the limiting metastable state for the liquid and the vapor of water at 100°C using the van der Waals equation of state.
What is the value of the efficiency of the adjacent reversible cycle displayed here in the T?s diagram of its working fluid? T/K 750 700 650 600 550 500 450 400 0 0.1 0.2 0.3 s/kJ/(kg. K) 0.4 0.5
Calculate the increase in thermal efficiency due to the introduction of a regenerating dearator in the Rankine-cycle power plant of Exercise 7.5. The plant operates at the optimal pressure (the
In the regenerative gas turbine power plant whose process flow diagram is shown in Figure 7.27a, the mass flow of air entering the compressor at 1 bar and 25?C is 17.9 kg/s. The pressure ratio of the
Compare the COP of the ammonia refrigeration system of Figure 7.21 to that of the single-stage system of Figure 7.20, operating with the same working fluid between the same minimum and maximum cycle
Consider a closed recuperative Brayton cycle turbine power plant employing supercritical CO2?as the working fluid. The working fluid at the compressor inlet is at T = 32?C and P = 7.7 MPa. CO2
Steam flows through a condenser at 2 × 106 kg/hr, entering as saturated vapor at 40°C, and leaving at the same pressure as subcooled liquid at 30°C. Cooling water enters the condenser pipes at
The fuel efficiency of reciprocating engines could be greatly increased (and thus pollution decreased) if the thermal energy that is wasted with the exhaust gases and by cooling the engine jacket and
The booster pump of a large steam power plant raises the pressure from 3 × 106 Pa at 313 K to 6 × 106 Pa. If the flow rate is 20 000 kg/min, and the isentropic efficiency is 0.75, calculate the
A renewable energy system for the (co)generation of electricity and cooling in sunny areas of the world consists of a solar Organic Rankine Cycle (ORC) power system, whose discharged thermal power is
Consider a two-stage gas compressor with inter-cooling.Assume the gas can be treated as ideal with constant specific heat. Derive an expression for the specific work input in terms of P1 ,P2 ,P4 ,?1
Calculate the thermal efficiency of a simple steam power plant implementing the superheated cycle configuration. Superheated steam enters the turbine at 10 MPa and 680 K. The pressure in the
A Rankine-cycle power plant has one stage of reheat. The steam at the turbine inlet is at 500°C and 3 × 106 Pa. After expansion to 0.5 × 106 Pa, the steam is reheated to 500°C, and
Consider an externally heated air gas turbine implementing the thermodynamic cycle described in Section 7.5. Using a compressor isentropic efficiency 0.85, determine the conversion efficiency of the
Determine the energy conversion efficiency of a supercritical steam power plant whose steam condenses at 310 K, and reaches 30 MPa in the primary heater. Assume that the inlet pump state is saturated
Determine the efficiency and the net mechanical power output of the system of Exercise 7.15 in the case where the compressor includes one inter-cooling stage, the isentropic efficiency of the
Combustion gas with the composition of Exercise 7.15 at the inlet of the reheated stages of a gas turbine is at 1400 K and 40 bar. The gas expands to atmospheric pressure. Between the high pressure
Determine the COP of a vapor-compression refrigerator implementing the simple inverse Rankine cycle, employing R134a as refrigerant, with saturated vapor leaving the evaporator at 278 K and saturated
A power system for space applications is based on a Rankine cycle using potassium as the working fluid. The working fluid at the turbine inlet is at 1200 K and 2.0 bar, and is fixed. The pump inlet
The compression ratio of an ideal Otto cycle using air as the working fluid is 8. The energy input is idealized as a transfer of energy as heat to the working fluid of 1650 kJ/kg. The inlet
An ideal diesel cycle using air as the working fluid has a compression ratio of 15. The energy input is idealized as a transfer of energy as heat to the working fluid of 1650 kJ/kg. The inlet
An idealized recip engine implementing the ideal Otto cycle operates with a compression ratio of 9:1 at intake conditions of 100 kPa and 298 K. The cylinder volume is initially 2000 cm3. If 4 kJ of
The compression ratio of an idealized recip engine implementing the ideal diesel cycle is 15:1. The air intake conditions are 100 kPa and 298 K. The cylinder volume is initially 2000 cm3. If 4 kJ of
A converging nozzle used in the stator of a high pressure steam turbine expands a steam mass flow rate of 1.0 kg/s. The nozzle inlet conditions of the steam are T = 500°C and P = 150 bar. The steam
Discuss why the idealized cycles of Exercises 7.20 and 7.21 are inadequate for the analysis of real engines. Which idealizations are likely to be the weakest? What effects will they have on the
Obtain the relation between the molar entropy change of an ideal gas vapor mixture and the molar entropy of each constituent.
Calculate the maximum power output of an adiabatic steam turbine in kW, whereby the mass flow rate of steam is 10 kg/s, the inlet is at 20 MPa and 400°C and the discharge pressure is 1 atm.
Potassium enters a turbine as saturated vapor at 1400 K and is discharged at 90 kPa. Calculate the minimum possible quality at the turbine outlet.
A solar-powered heat pump receives energy as heat from a solar collector at TH, rejects energy as heat to the atmosphere at TA, and pumps energy as heat from a cold space at TC. Derive an expression
Compute the maximum percent liquefaction (by mass) of O2 that can be achieved by expanding it adiabatically in a piston–cylinder system from the saturated vapor state at 10 atm to twice the initial
Consider the recuperator of the supercritical CO2 cycle power plant of Exercise 7.19 Assume that the energy rejected to the environment from the surface of the insulating material covering the
Nitrogen is contained in a closed pressurized vessel. The vessel and its contents are in thermal equilibrium with the environment at temperature T0 = 300 K. The environment pressure is P0 =
Derive the reference I-law cycle efficiency for the evaluation of the II-law efficiency of refrigeration systems.
Compute the standardized enthalpy and entropy of a mixture formed by an equal mass amount of CO2?and H2O at 2 atm and 311 K. If liquid is present for these conditions, assume that the vapor phase can
Obtain the expression for the specific flow exergy (9.5) from its definition.
Calculate the exergy associated with the drum of an industrial steam boiler that is shutting down. Assume all the mass flow rates of water in and out of the drum are negligible. The environment is at
The ammonia mass flow rate of the compressor of a refrigeration plant is 1 kg/s, and its inlet is at 266 K and 3 bar. The compressor outlet pressure is 16 bar while the outlet temperature is kept at
Perform the exergy analysis of the recuperated gas turbine of Exercise 7.15 knowing that i) The exergy input of the system is 14.26 MW, ii) The chemical exergy of the flue gas is 11 kJ/kg,
In a chemical process butane vapor is needed at some point. At that time 3 kg of butane are stored in a closed wellinsulated vessel in saturated conditions at 15.4 bar (100°C) and an electric heater
Determine the chemical equation for the reaction of octane (C8H18) with: a) 100 % excess air, and b) 250 % theoretical air.
Ammonia (NH3) and hydrogen (H2) have been proposed as automotive fuels as a way of reducing related pollution. Calculate a) The stoichiometric air/fuel ratio for these two fuels and compare it
Write out the chemical equation for the stoichiometric reaction of octane (C8H18) with air. Determine the theoretical air/fuel ratio for this reaction on both a volumetric (mole) and mass basis.
An oil-based fuel contains 84 % C and 16 % H2 by mass. Calculate the stoichiometric amount of air for complete combustion of 0.5 kg of fuel. Determine the air/fuel ratio.
Compute the air/fuel ratio by mass for the combustion of methane, if the exhaust gas dry analysis in percent by volume is: χCO2 = 0.01537, χO2 = 0.4917, χH2O = 0.03073. The presence of minor
Determine the dew point of the products of combustion of octane with 400 % theoretical dry air if the pressure is 0.1013 MPa.
Consider n-butane (C4H10) reacting stoichiometrically with dry air at a pressure of 125 kPa: determine the dew point. What is the effect of excess air if this reaction occurs with 100 % excess air?
A hydrocarbon whose composition is unknown undergoes combustion such that an Orsat apparatus measures the following composition: χCO2 = 0.09, χO2 = 0.088, χCO = 0.011, χN2 = 0.811.
Determine the adiabatic flame temperature for the combustion of propane in air if: (a) The air/fuel ratio is stoichiometric, (b) The air is twice the stoichiometric amount, and (c) The
If methane is burned in air and the excess air is 15 %, calculate the volume percent of oxygen in the flue gas, both on a wet basis (including water vapor) and on a dry basis (neglecting water vapor).
How much energy is released when 1 mole of propane (C3H8) reacts with 80 % theoretical air and both the inlet and the outlet of the combustor are kept at the standard reference state? How much energy
Make a table of the enthalpy of combustion at the standard reference state for hydrogen (H2), carbon monoxide (CO), methane (CH4), ethane(C2H6), and propane (C3H8), assuming that the water in the
Calculate the enthalpy of combustion for the so called water-gas shift reaction at standard reference conditions and at 300 ?C. CO(g) + H₂O(g)CO₂(g) + H₂(g),
Compare the energy released as heat by burning stoichiometrically 1 mole of CH4 with air and that released by burning 1 mole of C and 2 moles of H2. Assume that combustion occurs at the standard
Propane (C3H8) and oxygen in stoichiometric proportions react in a steady flow water-cooled burner. The reactants enter the burner at 305 K and leave the burner at 2 atm and emerge at 730 K. The flow
A laboratory analysis shows that CO2 becomes 10 % dissociated into CO and O2 at 2390 K if the total pressure is 1 atm. Obtain the equilibrium constant from this information and compare it to the
A turboprop engine has the following characteristics:The engine propels an airplane at 640 km/hr at an altitude of 7600 m (?35 ?C, 38 kPa). Analyze the thermodynamic cycle on a per kg basis, making
A gas turbine uses liquid n-butane (C4H10) as fuel. Calculate the required excess air such that the turbine inlet temperature does not exceed 1000 K. Assume for simplicity that the combustor inlet is
Find the mole fractions of O present in equilibrium O2 at 1000 K and at 5000 K. Assume P = 1 atm. Repeat the calculation for N2 and the same conditions.
Using data for standardized enthalpy and absolute entropy obtained from GASMIX calculate the equilibrium constant for the gaseous reaction ?298 K. Derive an expression which would let you obtain
The burner of a power station must provide thermal power to the boiler at a rate of 88 MW. The maximum flame temperature is to be 1100 K, and the products of combustion can leave the boiler at no
The water-gas shift reaction is ?Processes based on this reaction have been studied as a means of providing H2 as an automotive fuel. Assume that 1 mole of CO reacts with one mole of H2O at1800 K and
Hydrogen is to be burned with oxygen to produce a 1922 K flame. Neglecting dissociation, determine the composition of the product gases and specify the ratios of oxygen- and hydrogen-flow rates. The
Assuming that air is composed of O2 , O, N2, N, and NO, and that only O2 and N2 are present in significant amounts at room temperature in the ratio of 3.76 moles of N2 per mole of O2, determine
Calculate the equilibrium composition of the water-gas shift reaction of Exercise 10.25 with the element potential method. Compare the accuracy of the results with those obtained with the equilibrium
For the reaction?the equilibrium constant is log10?K = ?3.531 at 2000 K. Estimate the constant at T = 2225 K using the van t?Hoff equation. 1 H₂O = H₂+ = 0₂ 2
Consider the reaction (a) At the peak combustion temperature in a car (2500 to 2800 K), and neglecting the effect of pressure, will this reaction affect the production of NO??(b) If the peak pressure
Consider the reaction of air to form a gaseous mixture containing N2, O2 , and NO and assume that the perfect gas law is applicable. Calculate the mole fractions of the species at equilibrium at T =
One of the production processes of gallium-arsenide used in the semiconductor industry involves the equilibrium reaction of a gas mixture of As2 , As4, and Ga at 800 K and 0.1 atm, thus the
One mole of CO reacts with one mole of O2 in a steady flow process. Both reactants at the inlet are at 298 K and 1 atm. The final products of the reaction are a mixture of CO, CO2, and O2 at 1
Determine the maximum energy output per gmole of CO2 for a fuel cell operating on CO and O2 at 298 K and 1 atm. Assume that the products at the outlet of the fuel cell contain only CO2.
Obtain the relation between the isochoric specific heat of an ideal gas mixture and those of its constituents.
The following table reports the measurements of excess molar volume for the water– ethanol mixture at T = 298 K of Figure 8.4.Data on excess molar properties are often correlated with a polynomial
A gas having an ideal gas specific-heat ratio γ of 1.5 is required for a certain gas dynamics experiment. Specify a mixture that could be used.
The analysis of a gas mixture shows that the composition by weight is 15 % He, 60 % N2, and 25 % O2. Calculate the mole fractions and molecular weight of the mixture.
A mixture of gases used for a special heat transfer application consists of 25 % Ar, 50 % He, 25 % H2 by weight. The operating temperature is such that the mixture behaves like an ideal gas at the
A mixture of 40 % argon and 60 % nitrogen by weight is compressed from 1 atm, 20°C, to 4 atm. Assuming that the fluid complies with the ideal gas model, calculate the mixture temperature at the
The flue gas of a gas turbine contains water vapor and yH2O = 0.05. The temperature after the gas turbine outlet, downstream in the process, is 350 K. The flue gas contains minute quantities of
The excess enthalpy of a non-ideal liquid mixture is also often called heat of mixing or enthalpy of mixing, as it is the energy that gets transferred as heat to or from a mixture at constant
How many variables can be fixed independently in order to fix the state of a binary mixture in vapor–liquid equilibrium if, as is most often the case, the two phases contain both components in
Assume that a binary mixture and its components can be modeled using the van der Waals equation of state, both for the liquid and the vapor phase. Assume also that the mixture equation of state
A generic partial molar property is defined aswhere ϕ can be v, h, s,u, g, . . . ; if you are hasty, you might wrongly conclude that Ф = аф (а), a Ni T.P.N = а (Nф) a Ni T,P.Ng
A fluid formed by pentane and hexane obeys Raoult’s law quite well. Such a mixture can be used for example as the working fluid of an organic Rankine cycle power plant. The vapor pressure of pure
Use STANMIX to make a P–xy chart similar to that in Figure 8.20 for the equimolar methanol/water mixture. Plot the bubble and dew lines for T = 350 K, 375 K, and 400 K.
Use STANMIX to make a T–s chart similar to that in Figure 8.1 for the equimolar methanol/water mixture. Plot two iso-lines for each type, that is, isobar, isochore, isenthalp, iso-quality.

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