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engineering
introduction to chemical engineering thermodynamics
Introduction To Chemical Engineering Thermodynamics 2nd Edition HALDER - Solutions
A single-stage compressor is used to compress \(1000 \mathrm{~m}^{3} / \mathrm{hr}\) of air at \(100 \mathrm{kPa}\) and \(300 \mathrm{~K}\) to \(600 \mathrm{kPa}\). The isentropic efficiency of the compressor is \(80 \%\). Estimate the power input to the compressor. Take \(\gamma=1.3\).
A nozzle, to which steam at \(500 \mathrm{kPa}\) and \(623 \mathrm{~K}\) is entering at the rate of \(12 \mathrm{~kg} / \mathrm{s}\) and leaving at \(500 \mathrm{kPa}\) and \(523 \mathrm{~K}\), is fitted to a long pipe. The amount of heat loss to the environment is calculated to be \(120
Air enters an adiabatic compressor at \(100 \mathrm{kPa}\) and \(300 \mathrm{~K}\) at a rate of \(0.5 \mathrm{~m}^{3} / \mathrm{s}\) and leaves at \(600 \mathrm{kPa}\). Air is assumed to behave as an ideal gas. Determine the work of compression per unit mass for(a) Reversible adiabatic compression
An ideal gas enters a high-velocity nozzle which operates at \(1000 \mathrm{kPa}\) and \(600 \mathrm{~K}\). The inlet velocity of the gas at the nozzle is \(50 \mathrm{~m} / \mathrm{s}\). Assume that the heat capacity ratio, \(\gamma=1.4\) and the molecular weight of the gas \(=17\). Determine (i)
Deduce the expression on the work of compression in a two stage compression system.
Air enters an adiabatic compressor at \(150 \mathrm{kPa}\) and \(350 \mathrm{~K}\) at a rate of \(0.8 \mathrm{~m}^{3} / \mathrm{s}\) and leaves at \(700 \mathrm{kPa}\) and \(500 \mathrm{~K}\). Neglecting the changes in kinetic and potential energy, estimate the power input to the compressor.
Steam at \(800 \mathrm{kPa}\) and \(773 \mathrm{~K}\) enters a nozzle with an enthalpy of \(3480 \mathrm{~kJ} / \mathrm{kg}\) and leaves at \(100 \mathrm{kPa}\) and \(573 \mathrm{~K}\) with an enthalpy of \(3074 \mathrm{~kJ} / \mathrm{kg}\).(a) If the initial enthalpy of the steam is negligible,
Derive an expression on the work done in an adiabatic reversible compression process.
\(\mathrm{CO}_{2}\) at \(100 \mathrm{kPa}\) and \(330 \mathrm{~K}\) is to be compressed steadily in an adiabatic compressor to \(500 \mathrm{kPa}\) and \(450 \mathrm{~K}\). The mass flow rate of air is \(0.05 \mathrm{~kg} / \mathrm{s}\). Assuming that the changes in the kinetic and potential
Exhaust steam at \(100 \mathrm{kPa}\) and \(200^{\circ} \mathrm{C}\) enters the subsonic diffuser of a jet engine steadily with a velocity of \(190 \mathrm{~m} / \mathrm{s}\). The inlet area of the diffuser is \(2000 \mathrm{~cm}^{2}\). The steam leaves the diffuser with a velocity of \(70
What is the significance of inter-stage cooling in multistage compression?
A two-stage compressor is used to compress \(\mathrm{CO}_{2}\) at a rate of \(500 \mathrm{~m}^{3} / \mathrm{hr}\) from an initial state of \(100 \mathrm{kPa}\) and \(300 \mathrm{~K}\) to an exit pressure of \(700 \mathrm{kPa}\). Determine the power required to run the compressor. Take
Develop the energy balance equation for (i) the whole heat exchanger as a control volume and (ii) only one fluid as a control volume.
Explain the operation methodology of a nozzle. Mention the application areas of a nozzle and a diffuser.
What is the working principle of an ejector? Mention the uses of ejectors.
Prepare a mass and energy balance for the unsteady flow process.
What is Mach number? How does it play an important role in establishing the relation between the velocity and the cross-sectional area for a nozzle?
A Carnot refrigerator is used to maintain a food compartment at -4C. Heat is released from the compartment to a room at 30C. If 35 kW heat is removed, determine(a) The coefficient of performance of the cycle;(b) The power required;(c) The rate of heat released to the room.
How do you judge the performance capability of a refrigerator?
A Carnot refrigerator is used to keep a food compartment at \(-2^{\circ} \mathrm{C}\). Heat is rejected from the compartment to a room at \(35^{\circ} \mathrm{C}\). If \(40 \mathrm{~kW}\) heat is removed, determine(a) The coefficient of performance of the cycle(b) The power required(c) The rate of
Define the term ton of refrigeration. Can it be expressed in kilowatts?
(a) A one-ton Carnot refrigerating machine is used to keep a refrigerated space at the temperature of \(-10^{\circ} \mathrm{C}\), while the environment is at \(45^{\circ} \mathrm{C}\). Determine the power consumption of the machine.(b) If the machine is used to maintain a freezer box at the
Assume that the Carnot refrigerating machine in Example 8.2 is of unknown capacity. Considering both parts(a) and (b), what would be the increase in the percentage of work input required for the freezer box over the refrigerated space for the same extent of refrigerating effect?Example 8.2(a) A
To maintain a freezer box at \(-40^{\circ} \mathrm{C}\) on a summer day when the ambient temperature is \(27^{\circ} \mathrm{C}\), heat is removed at the rate of \(1.25 \mathrm{~kW}\). What is the maximum possible coefficient of performance of the freezer, and what is the minimum power that must be
What is a heat pump? How can it be used for heating a room during winter?
A Carnot refrigerator used for air-conditioning operates between a low temperature of \(5^{\circ} \mathrm{C}\) and a high temperature of \(45^{\circ} \mathrm{C}\). Now, if it is used for maintaining foodstuffs in a cold storage operating at a low temperature of \(-15^{\circ} \mathrm{C}\), and a
A Carnot heat pump is used to maintain a temperature of \(24^{\circ} \mathrm{C}\) inside a building when the outside temperature is \(0^{\circ} \mathrm{C}\). The amount of heat supplied by the heat pump is \(25 \mathrm{~kW}\). Estimate the co-efficient of performance and the power input of the heat
Explain the dual operation of a heat pump during winter and summer.
In peak winter, it is desired to heat a house with the help of a heat pump when the temperature of outside air is \(-2^{\circ} \mathrm{C}\). If the inside of the house is maintained at \(20^{\circ} \mathrm{C}\) and the house loses \(80,000 \mathrm{~kJ} / \mathrm{h}\), what is the minimum power
An inventor claims to have developed a refrigerator, that maintains the refrigerated space at \(1{ }^{\circ} \mathrm{C}\) while operating in a room where the temperature is \(30^{\circ} \mathrm{C}\), and that has a COP of 11. Is this claim reasonable?
Prove that \(\mathrm{COP}_{\mathrm{HP}}=\mathrm{COP}_{\mathrm{R}}+1\).
A refrigerant using refrigerant R-12 as the working fluid operates on vapourcompression cycle between \(273 \mathrm{~K}\) and \(313 \mathrm{~K}\). Compute the following:(i) COP of the vapour-compression cycle(ii) Refrigerating effect(iii) COP of an ideal Carnot refrigerator(iv) Work of compression
A Carnot refrigerator is used to keep a freezer at \(-2^{\circ} \mathrm{C}\). If the room to which the heat is rejected is at \(35^{\circ} \mathrm{C}\), calculate for a heat removal rate of \(2 \mathrm{~kW}\)(a) The COP of the cycle(b) The power required(c) The rate of heat rejected to the room.
Can the COP of a refrigerator be greater than unity? Why?
(a) A one-ton Carnot refrigerator maintains a cold space at a temperature of \(-15^{\circ} \mathrm{C}\), while the surroundings are at \(40^{\circ} \mathrm{C}\). Determine the power consumption of the refrigerator.(b) If the same refrigerator is used as a freezer maintaining a temperature of
A vapour-compression refrigeration cycle in which the refrigerant HFC-134a enters the compressor as superheated vapour at \(0.18 \mathrm{MPa}\) and \(-10^{\circ} \mathrm{C}\) at a rate of \(0.06 \mathrm{~kg} / \mathrm{s}\) and leaves at \(1.0 \mathrm{MPa}\) and \(45^{\circ} \mathrm{C}\). The
A vapour-compression refrigeration system using CFC-12 (Freon) rated at 5 tons is employed in a chemical manufacturing plant to maintain the temperature of evaporator and condenser at \(-10^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\) respectively. The isentropic efficiency of compressor is
How does a refrigerator differ from a heat pump?
In winter, when the outside temperature is \(0^{\circ} \mathrm{C}\), a room is to be maintained at \(25^{\circ} \mathrm{C}\). The heat loss from the room is estimated to be \(5 \mathrm{~kW}\). Two alternative strategies to keep the room temperature constant are:(a) direct electrical heating and(b)
A large auditorium is desired to be maintained at \(20^{\circ} \mathrm{C}\) in both summer and winter seasons. In winter, the temperature of the environment is \(4^{\circ} \mathrm{C}\) while the same in summer is \(38^{\circ} \mathrm{C}\). The energy loss through the barrier walls of the auditorium
Justify the statement: A refrigerating machine works on the principle of the second law of thermodynamics.
An inventor claims to have developed an absorption refrigerating machine that receives heat from a source at \(125^{\circ} \mathrm{C}\) and maintains the refrigerated space at \(-5^{\circ} \mathrm{C}\) and have a COP of 2 . If the environment temperature is \(28^{\circ} \mathrm{C}\), can this claim
Name the different operational steps carried out in a Carnot cycle.
A heat pump is used to maintain a temperature of \(20^{\circ} \mathrm{C}\) inside a building when the outside temperature is \(-2^{\circ} \mathrm{C}\). The amount of heat supplied by the heat pump is \(35 \mathrm{~kW}\). Estimate the coefficient of performance and the power input of the heat pump.
An air refrigeration system of 5 tons cooling capacity is employed to maintain the temperature of a refrigerated space at \(-20^{\circ} \mathrm{C}(253 \mathrm{~K})\) when the temperature of the surroundings is \(30^{\circ} \mathrm{C}(303 \mathrm{~K})\). The pressure ratio of the compressor is 4 .
With the help of \(T-S\) diagram, explain the functioning of a Carnot refrigerator.
A Carnot heat pump supplies \(25 \mathrm{~kW}\) of heat at \(25^{\circ} \mathrm{C}\) when the environment temperature is \(0^{\circ} \mathrm{C}\). Calculate the COP and the power input.
With the help of a neat sketch, explain the working principle of a vapour-compression refrigeration cycle and find its COP.
Consider an ideal gas refrigeration cycle using air as the working fluid which is used to maintain a cold space at \(-15^{\circ} \mathrm{C}\) while discarding the heat to the environment at \(30^{\circ} \mathrm{C}\). The pressure ratio of the compressor is 4 . Take \(C_{P}=1.007 \mathrm{~kJ} /
Name some refrigerants used widely in the vapour-compression cycle.
A vapour-compression refrigeration unit using steam as the working fluid operates between \(306 \mathrm{~K}\) and \(280 \mathrm{~K}\). The enthalpy of saturated vapour at \(280 \mathrm{~K}\) is \(2514.20 \mathrm{~kJ} / \mathrm{kg}\) and the enthalpy of saturated liquid at \(306 \mathrm{~K}\) is
What are the important factors to be taken into account for selecting a promising refrigerant in the present scenario of replacement of CFCs?
A vapour-compression refrigeration system based on CFC-12 operates between an evaporator temperature of \(245 \mathrm{~K}\) and a condenser temperature of \(310 \mathrm{~K}\). The power input to the compressor is \(55 \mathrm{~kW}\). Determine the cooling capacity and the COP of the system, given
What desirable properties should a refrigerant possess?
Determine the COP of a vapour-compression refrigeration system that uses Freon-12 as working fluid and operates between a condensation temperature of \(45^{\circ} \mathrm{C}\) and an evaporator temperature of \(-20^{\circ} \mathrm{C}\). Also determine the theoretical power consumption if the
Explain the operation that takes place in a vapour-absorption cycle.
An ammonia refrigeration plant is to operate between a saturated liquid at \(313 \mathrm{~K}\) at the condenser outlet and a saturated vapour at \(283 \mathrm{~K}\) at the evaporator outlet. If the capacity of the refrigeration plant is desired to the tune of 6 tons, compute(a) The coefficient of
Provide a proper comparative discussion of between vapour-compression and vapourabsorption cycles.
A vapour-compression refrigerating machine uses HFC-134a as the working fluid. The fluid enters the compressor as superheated vapour at \(0.18 \mathrm{MPa}\) and \(-10^{\circ} \mathrm{C}\) and leaves at a rate of \(0.9 \mathrm{MPa}\) and \(50^{\circ} \mathrm{C}\). The mass flow rate of the working
Enumerate the various application areas of refrigeration.
An absorption refrigeration system receives heat from a source at \(120^{\circ} \mathrm{C}\) and maintains the space which is to be cooled at \(1^{\circ} \mathrm{C}\). The temperature of the surroundings is \(26^{\circ} \mathrm{C}\). What is the maximum coefficient of performance that could be
What are the advantages and disadvantages of the air refrigeration cycle?
In a remote place, the heat energy is supplied to an absorption refrigeration system from a solar pond at \(125^{\circ} \mathrm{C}\) at the rate of \(4.5 \times 10^{5} \mathrm{~kJ} / \mathrm{h}\). The environment is at \(28^{\circ} \mathrm{C}\) and the cold space is maintained at \(-5^{\circ}
What are the different processes employed for liquefying a gas?
An ideal air refrigeration cycle is operated at the upper temperature of \(35^{\circ} \mathrm{C}\) and the lower temperature of \(-20^{\circ} \mathrm{C}\). The COP of the cycle is 3 . Determine the work of the expander, the work of the compressor, and the net work of the cycle. Also estimate the
Compare the Linde process with the Claude process for air liquefaction.
It is planned to maintain a cold storage at \(-10^{\circ} \mathrm{C}\) by employing an air refrigeration system which absorbs \(900 \mathrm{~kJ} / \mathrm{min}\). The temperature of ambient water is \(20^{\circ} \mathrm{C}\) after compression at \(492.5 \mathrm{kPa}\) and is later expanded to
Mention the usefulness of liquefaction processes.
An air refrigeration cycle has a pressure ratio of 5. Air enters the compressor at \(12^{\circ} \mathrm{C}\) and the turbine at \(48^{\circ} \mathrm{C}\). The mass flow rate of air is \(0.08 \mathrm{~kg} / \mathrm{s}\). Take \(C_{P}=1.007 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\) and \(\gamma=1.4\).
Why are the CFCs still in major use despite having a strong negative impact on the environment?
A Bell-Coleman refrigeration cycle operates between the pressures of \(50 \mathrm{kPa}\) and 250 \(\mathrm{kPa}\). Air enters the compressor at \(288 \mathrm{~K}\) and the turbine at \(313 \mathrm{~K}\). The air flow rate is \(0.08 \mathrm{~kg} / \mathrm{s}\). Take \(C_{P}=1.008 \mathrm{~kJ} /
The Brayton refrigeration cycle works on the principle of air standard refrigeration and uses air as the working fluid. The pressure ratio of the compressor is 5. At the compressor inlet, the pressure is \(100 \mathrm{kPa}\) and the temperature is \(308 \mathrm{~K}\). Determine the work of
Calculate the partial molar volume of water in a \(70 \mathrm{~mol}\) per cent ethanol-water solution, in which the partial molar volume of ethanol is \(61.23 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\), given that the density of the mixture is \(901.57 \mathrm{~kg} / \mathrm{m}^{3}\).
Calculate the partial molar volume of water in a \(50 \mathrm{~mol}\) per cent ethanol-water solution in which the partial molar volume of ethanol is \(52.37 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{mol}\). Given that the density of the mixture is \(800.21 \mathrm{~kg} / \mathrm{m}^{3}\).
What is partial molar property? What is its significance in describing a multicomponent system? How do you differentiate between molar volume and partial molar volume?
It is desired to prepare \(2.5 \mathrm{~m}^{3}\) of a \(60 \mathrm{~mol}\) per cent methanol-water solution. Determine the volumes of methanol and water required to be mixed at ambient temperature, given that the partial molar volumes of methanol and water are \(58.3 \times 10^{-6} \mathrm{~m}^{3}
In order to prepare \(2.0 \mathrm{~m}^{3}\) of alcohol-water solution, alcohol of mole fraction \(X_{1}=0.40\) is required to be mixed with water at \(25^{\circ} \mathrm{C}\). Determine the volumes of alcohol and water needed to prepare the mixture. Given that Partial molar volume of alcohol
Show that for an ideal gas the partial molar volume in a mixture of two gases is equal to \(\frac{R T}{P}\) and this is true for all the components of a mixture of ideal gases.
In order to prepare \(3.0 \mathrm{~m}^{3}\) of an alcohol-water solution, alcohol of mole fraction \(X_{1}=\) 0.60 is required to be mixed with water at \(25^{\circ} \mathrm{C}\). Determine the volumes of alcohol and water needed to prepare the mixture, given that Partial molar volume of methanol
A student experimenter decides to convert \(2000 \mathrm{~cm}^{3}\) of laboratory alcohol containing \(96 \%\) ethanol and \(4 \%\) water by mass into vodka having a composition of \(56 \%\) ethanol and \(44 \%\) water by mass.Data given:At \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\)In \(96
Describe the 'method of intercept' to determine the partial molar properties of the components in a binary mixture.
Acetone and chloroform are mixed to prepare \(1.0 \mathrm{~kg}\) of a solution in which the mole fraction of chloroform \(\left(x_{2}\right)\) is 0.4690 , the partial molar volume of chloroform is \(80.235 \mathrm{~cm}^{3} / \mathrm{mol}\), and that of acetone is \(74.166 \mathrm{~cm}^{3} /
In a binary liquid system, the enthalpy of species 1 and 2 at constant temperature and pressure is represented by the following equation:\[ H=400 x_{1}+600 x_{2}+x_{1} x_{2}\left(40 x_{1}+20 x_{2}\right) \quad \text { where } H \text { is in } \mathrm{J} / \mathrm{mol} \]Determine the expressions
What do you mean by chemical potential? Show that the variation of the chemical potential of a component \(i\) with pressure is given by \(d \mu_{i}=\bar{V}_{i} d P\).
It is desired to prepare \(2000 \mathrm{~cm}^{3}\) of an antifreeze solution consisting of \(30 \mathrm{~mol}\) per cent methanol in water. What volumes of pure methanol and pure water at \(25^{\circ} \mathrm{C}\) must be mixed to form the required volume of antifreeze, also at \(25^{\circ}
The molar volume of a binary mixture consisting of components 1 and 2 at \(298 \mathrm{~K}\) and \(1 \mathrm{~atm}\) is represented by the following empirical relation:\[ V=52.36-32.64 y_{2}-42.98 y_{2}^{2}+58.77 y_{2}^{3}-23.45 y_{2}^{4} \]where \(V\) is in \(\mathrm{cm}^{3} / \mathrm{mol}\) and
Define chemical potential in terms of internal energy, enthalpy, work function, and Gibbs function.
If the molar density of a binary mixture is given by the empirical expression\[ ho=a_{0}+a_{1} x_{1}+a_{2} x_{1}^{2} \]Find the corresponding expressions for \(\bar{V}_{1}\) and \(\bar{V}_{2}\).
The partial molar volume of water (1) in its mixture with methanol (2) at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) can be approximated by:where \(a=-3.2 \mathrm{~cm}^{3} / \mathrm{mol}\).\[ \bar{V}_{1}=18.1+a x_{2}^{2} \]Develop an expression for the partial molar volume of methanol at the
Which of the following derivatives are partial molar properties?(a) \(\left(\frac{\partial V}{\partial n_{i}}\right)_{T, P, n_{j}}\)(b) \(\left(\frac{\partial P}{\partial n_{i}}\right)_{T, V, n_{j}}\)(c) \(\left(\frac{\partial G}{\partial n_{i}}\right)_{V, P, n_{j}}\)(d) \(\left(\frac{\partial
The molar volume of a binary mixture containing benzene and cyclohexane is represented by the empirical relation\[ V=109.4 \times 10^{-6}-16.8 \times 10^{-6} x-2.64 \times 10^{-6} x^{2} \]where \(V\) is in \(\mathrm{cm}^{3} / \mathrm{mol}\) and \(x\) is the mole fraction of component 1 . Find the
The molar volumes of a binary solution at \(25^{\circ} \mathrm{C}\) are measured as given below:Using the methods of tangential intercept, calculate the partial molar volumes of components 1 and 2 at(a) \(X_{1}=0.5\)(b) \(X_{1}=0.75\). X 0 0.2 0.4 0.6 0.8 1.0 V x 10 (m/mol) 20.0 21.5 24.0 27.4 32.0
Derive an expression for the change in chemical potential with pressure for an ideal gas.
The molar volume of a binary mixture is given by\[ V=y_{1} V_{1}+y_{2} V_{2}+y_{1} y_{2}\left[A+B\left(y_{1}-y_{2}\right)\right] \]Determine the partial molar volumes of components 1 and 2 .
The activity coefficient of component 1 in a binary solution is represented by\[ \ln \gamma_{1}=a x_{2}^{2}+b x_{2}^{3}+c x_{2}^{4} \]where \ (a, b\), and \(c\) are constants independent of concentrations. Obtain an expression for \(\gamma_{2}\) in terms of \(x_{1}\).
Prove the following statement: At the same temperature and pressure, the chemical potential or partial molar free energy of a component in every phase must be the same under equilibrium conditions.
Prove that the chemical potential of the \(i\) th component in an ideal gas mixture is given by\[ \mu_{i}=\mu_{i}^{0}+R T \ln \frac{p_{i}}{p^{0}} \]
For a binary system, if the activity coefficient of component is \(\ln \gamma_{1}=a x_{2}^{2}\), then derive the expression for component 2.
Explain the influence of temperature and pressure on chemical potential.
Estimate the fugacity of liquid \(n\)-octane at \(427.85 \mathrm{~K}\) and \(1.0 \mathrm{MPa}\). The saturation pressure of \(n\)-octane at \(427.85 \mathrm{~K}\) is \(0.215 \mathrm{MPa}\).
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