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advanced thermodynamics for engineers

Questions and Answers of Advanced Thermodynamics For Engineers

A stoichiometric mixture of carbon monoxide and air reacts in a combustion chamber, forms exhaust products at \(3000 \mathrm{~K}\) and 1 bar. If the products are in chemical equilibrium, but no
A mixture containing hydrogen and oxygen in the ratio of \(2: 1\) by volume is contained in a rigid vessel. This is ignited at \(60{ }^{\circ} \mathrm{C}\) and a pressure of \(1 \mathrm{~atm}(1.013
A vessel is filled with hydrogen and carbon dioxide in equal parts by volume and the mixture is ignited. If the initial pressure and temperature are \(2 \mathrm{bar}\) and \(60^{\circ} \mathrm{C}\)
A stoichiometric mixture of hydrogen and air is compressed to 18.63 bar and \(845^{\circ} \mathrm{C}\). It burns adiabatically at constant volume. Show that the final equilibrium temperature is
A mixture containing equal volumes of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) and hydrogen \(\left(\mathrm{H}_{2}\right)\) is contained in a rigid vessel. It is ignited at \(60^{\circ}
A gas turbine combustion chamber receives air at 6 bar and \(500 \mathrm{~K}\). It is fuelled using octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) at an equivalence ratio of 0.8 (i.e. weak),
A mixture of one part by volume of vapourised benzene to 50 parts by volume of air is ignited in a cylinder and adiabatic combustion ensues at constant volume. If the initial pressure and temperature
A gas engine is operated on a stoichiometric mixture of methane \(\left(\mathrm{CH}_{4}\right)\) and air. At the end of the compression stroke, the pressure and temperature are \(10 \mathrm{bar}\)
A gas injection system supplies a mixture of propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) and air to a spark-ignition engine, in the ratio of volumes of 1:30. The mixture is trapped at \(1
A \(10 \%\) rich mixture of heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right)\) and air is trapped in the cylinder of an engine at a pressure of \(1 \mathrm{bar}\) and temperature of \(400
A turbocharged, intercooled compression ignition engine is operated on octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) and achieves constant pressure combustion. The volumetric compression
A gas engine with a volumetric compression ratio of \(10: 1\) is run on a weak mixture of methane \(\left(\mathrm{CH}_{4}\right)\) and air, with \(\phi=0.9\). If the initial temperature and pressure
One method of reducing the maximum temperature in an engine is to run with a rich mixture. A spark-ignition engine with a compression ratio of 10:1, operating on the Otto cycle, runs on a rich
A reaction in which the pre-exponential term is independent of temperature is found to be a 100 times faster at \(200^{\circ} \mathrm{C}\) than it is at \(25^{\circ} \mathrm{C}\). Calculate the
A chemical reaction is found to be 15 times faster at \(100^{\circ} \mathrm{C}\) than at \(25^{\circ} \mathrm{C}\). Measurements show that the pre-exponential term contains temperature to the power
The rate of formation of nitric oxide (NO) is controlled by the three reversible chemical reactionsUse the steady state approximation for the nitrogen atom concentration and the assumption of partial
The rate of change of mole concentration of constituent \(A\) in a chemical reaction is expressed as\[\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=-k[\mathrm{~A}]^{\mathrm{n}}\]While mole
(a) What is meant by the terms(i) a global reaction;(ii) an elementary reaction;(iii) a reaction mechanism.(b) Describe the steps required to form a chain reaction and explain why chain reactions are
A combustible mixture of gas and air is contained in a well-insulated combustion bomb. It is ignited at a point and a thin flame propagates through the mixture completely burning the reactants. This
The structure of ethylene is \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}\). Estimate the enthalpy of reaction when \(1 \mathrm{kmol}\) of ethylene is completely oxidised. Compare the value obtained
Describe the construction of a boiler for burning pulverised coal. Explain how this design optimises the temperature, turbulence and time required for good combustion. What are the main emissions
(a) One of the main problems encountered in the design of a diesel engine combustion system is the mixing of the air and fuel sufficiently rapidly to ensure complete combustion. Explain, using
A method of reducing (improving) engine fuel consumption and reducing the emissions of \(\mathrm{NO}_{\mathrm{x}}\) in a spark-ignition engine is to run it lean, i.e. with a weak mixture. Discuss the
Calculate the ignition delay period (in deg ca) in a diesel engine using Eqns (16.15a) and (16.15b) using the conditions at the beginning of fuel injection that exist after compression in the engine
This question is based on Fig. 16.9. An engine operating on an Otto cycle has a maximum peak pressure of \(60 \mathrm{bar}\). If the pressure and temperature at the beginning of the cycle are 1.0 bar
Compare the air-standard cycle thermal efficiencies of an Otto cycle obtained by calculating the state points around the cycle with the value obtained from Eqn (3.16) for an 'engine' operating with a
Compare the air-standard cycle thermal efficiencies of a diesel cycle obtained by calculating the state points around the cycle with the value obtained from Eqn (3.20) for an 'engine' operating with
Recalculate the Otto cycle in P16.5 using EQUIL2 to evaluate the conditions around the cycle. Do these calculations both with and without considering dissociation. How has the use of more accurate
Recalculate the diesel cycle in P16.6 using EQUIL2 to evaluate the conditions around the cycle. Do these calculations both with and without considering dissociation. How has the use of more accurate
Provide mechanical and molecular definitions of work and heatminor effect on the principles being illustrated). Assume compression ratio \(=9.0: 1\);
A gas turbine engine operates between minimum temperature \(T_{1}\) and maximum temperature \(T_{3}\). Show that the optimum pressure ratio for maximum work output
A gas turbine engine operates at temperature between 300 and \(1200 \mathrm{~K}\). The pressure ratio is 12 and the working fluid is \(\mathrm{CO}_{2}\). Assume an isentropic process,(1) Determine
Assume the maximum pressure ratio. Determine the efficiency and work ratio of the cycle in P17.1.\([0.75,0\).P17.1.A gas turbine engine operates between minimum temperature \(T_{1}\) and maximum
Air at \(290 \mathrm{~K}\) flows into the compressor of a gas turbine engine. The temperature increases to \(1350 \mathrm{~K}\) when it flows into the turbine. The pressure ratio is 15 and power
A gas turbine operates at a pressure ratio of 8 . The air flows into the compressor at \(290 \mathrm{~K}\) and flows out of the combustion chamber at \(1400 \mathrm{~K}\). The efficiency of
Prove that the optimum pressure ratio for intercooling of gas turbines with heat exchange is given below:\[\frac{p_{2}}{p_{1}}=\frac{p_{i}}{p_{1}}=\left(\frac{p_{2^{\prime}}}{p_{1}}\right)^{1 /
Air flows into the compressor of a gas turbine engine at \(0.1 \mathrm{MPa}, 300 \mathrm{~K}\) and is compressed to \(0.8 \mathrm{MPa}\). The air is heated to a maximum temperature of \(1100
A turbojet is travelling at high Mach number and the ambient pressure, \(p_{\mathrm{a}}\), and temperature, \(T_{\mathrm{a}}\), are 0.5 bar and \(220 \mathrm{~K}\) respectively. It is also known that
Show that the Joule-Thomson coefficient, \(\mu\), is given by\[\mu=\frac{1}{c_{p}}\left(T\left(\frac{\partial v}{\partial T}\right)_{p}-v\right)\]Hence or otherwise show that the inversion
The last stage of a liquefaction process is shown in diagrammatic form in Fig. P18.2. Derive the relationship between \(p_{1}\) and \(T_{1}\) for the maximum yield of liquid at conditions \(p_{L},
The equation of state for a certain gas is\[v_{m}=\frac{\Re T}{p}+\frac{k}{\Re T}\]where \(k\) is a constant. Show that the variation of temperature with pressure for an isenthalpic process from 1 to
A gas has the equation of state\[\frac{p v_{m}}{\Re T}=1+\mathrm{A} p\left(T^{3}-9.75 T_{\mathrm{c}} T^{2}+9 T_{\mathrm{c}}^{2} T\right)+\mathrm{B} p^{2} T\]where \(\mathrm{A}\) and \(\mathrm{B}\)
A gas has the equation of state\[\frac{p v_{m}}{\Re T}=1+N p+M p^{2}\]where \(N\) and \(M\) are functions of temperature. Show that the equation of the inversion curve is\[p=-\frac{\mathrm{d}
In a simple Linde gas-liquefaction plant (see Fig. 18.13), air is taken in at the ambient conditions of 1 bar and \(300 \mathrm{~K}\). The water-jacketed compressor delivers the air at 200 bar and
A process plant has two streams of hot fluid and two streams of cold fluid, as defined in Table P19.1. It is required to minimise the energy which must be transferred to hot and cold utilities by
Some stream data have been collected from a process plant, and these are listed in Table P19.2. Assuming the minimum temperature difference between streams, \(\Delta T_{\min }=10^{\circ}
Figure P19.3 shows a network design using steam, cooling water and some heat recovery.(a) Does this design achieve the minimum energy target for \(\Delta T_{\min }=20^{\circ} \mathrm{C}\) ?(b) If the
Figure P19.4 shows two hot streams and two cold streams for heat integration (subject to \(\Delta T_{\min }=20^{\circ} \mathrm{C}\) ).(i) What are the energy targets?(ii) Show a network design
Figure P19.5 shows an existing design of a process plant, containing two exothermic processes. These require streams of reactants as shown in the diagram, and produce products at the temperatures
Recalculate the problem in P19.5 using a \(\Delta T_{\min }=10{ }^{\circ} \mathrm{C}\). Comment on the effect of reducing the minimum temperature difference.[(a) \(T_{\mathrm{C}_{\text {pinch
A network for a process plant is shown in Fig P19.7.(a) Calculate the energy targets for \(\Delta T_{\min }=10{ }^{\circ} \mathrm{C}\) and show a design that achieves these targets.(b) Explain why
The emf of a copper-iron thermocouple caused by the Seebeck effect, with a cold junction at \(0{ }^{\circ} \mathrm{C}\), is given by\[\varepsilon=\alpha_{1} t+\frac{\alpha_{2}}{2}
The emf of a copper-iron thermocouple with its cold junction at \(0{ }^{\circ} \mathrm{C}\) is given by\[\varepsilon=-13.403 t+0.0138 t^{2}+0.0001 t^{3} \quad \mu \mathrm{V}\]where \(t=\) temperature
A fluid consisting of a single component is contained in two containers at different temperatures. Show that the difference in pressure between the two containers is given by\[\frac{\mathrm{d}
A thermocouple is connected across a battery, and a current flows through it. The cold junction is connected to a reservoir at \(0{ }^{\circ} \mathrm{C}\). When its hot junction is connected to a
A pure monatomic perfect gas with \(c_{p}=5 \Re / 2\) flows from one reservoir to another through a porous plug. The heat of transport of the gas through the plug is \(-\Re T / 2\). If the system is
A thermal conductor with constant thermal and electrical conductivities, \(k\) and \(\lambda\) respectively, connects two reservoirs at different temperatures and also carries an electrical current
A thermal conductor of constant cross-sectional area connects two reservoirs which are both maintained at the same temperature, \(T_{0}\). An electric current is passed through the conductor, and
An electric cell has the following chemical reaction\[\mathrm{Zn}(\mathrm{s})+2 \mathrm{AgCl}(\mathrm{s})=\mathrm{ZnCl}_{2}+2 \mathrm{Ag}(\mathrm{s})\]and produces an emf of \(1.005 \mathrm{~V}\) at
An electric cell is based on the reaction \(\mathrm{Pb}+\mathrm{Hg}_{2} \mathrm{Cl}_{2} \rightarrow \mathrm{PbCl}_{2}+2 \mathrm{Hg}\). If the enthalpy of reaction for this reaction, \(Q_{p}\), at
Calculate the emf of a hydrogen-oxygen fuel cell operating reversibly if the overall reduction in Gibbs energy is \(238 \mathrm{MJ} / \mathrm{kg} \mathrm{H}_{2}\). If the cell operates at \(75 \%\)
An ideal, isothermal, reversible fuel cell with reactants of oxygen and hydrogen, and a product of water operates at a temperature of \(400 \mathrm{~K}\) and a pressure of 1 bar. If the operating
A hydrogen-oxygen fuel cell is required to produce a constant voltage and operate over a pressure range of \(0.125-10\) bars. The datum voltage is \(1.16 \mathrm{~V}\) at a temperature of \(350
A hydrogen-oxygen fuel cell operates at a temperature of \(450 \mathrm{~K}\) and the reactants and products are all at a pressure of 3 bar. Due to internal resistances the emf of the cell is only

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