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engineering
introduction to chemical engineering thermodynamics
Questions and Answers of
Introduction To Chemical Engineering Thermodynamics
During the adiabatic compression of a gas in a cylinder, the temperature of the gas rises by \(30^{\circ} \mathrm{C}\). Express the rise in temperature in terms of the Fahrenheit, Kelvin and Rankine
What is the criterion for a thermodynamic system to be at steady state?
Determine the work done while a body of mass \(47 \mathrm{~kg}\) is lifted through a distance of \(20 \mathrm{~m}\). Also calculate the power. The entire process takes time to the tune of \(3
What is the difference between steady and uniform states?
An arbitrary temperature scale is proposed, in which \(20^{\circ}\) is assigned to the ice point and \(75^{\circ}\) is assigned to the steam point. Derive an equation relating this scale to the
State the zeroth law of thermodynamics. How does it play an important role in measuring temperature?
If a Celsius temperature is two-thirds the corresponding Fahrenheit temperature, determine both the temperatures.
State the phase rule and show how it can be mathematically expressed. What is the importance of degree of freedom? Find the value of degree of freedom for the water system.
A skin diver descends to a depth of \(30 \mathrm{~m}\) in a salt lake where the density is \(1030 \mathrm{~kg} / \mathrm{m}^{3}\). What is the pressure on the diver's body at this depth?
A tank contains \(400 \mathrm{~kg}\) of a fluid. If the volume of the tank is \(2.5 \mathrm{~m}^{3}\), then what is the density of the fluid and what is the specific gravity?
Differentiate between state function and path function. Prove that internal energy is a state function and work is a path function.
Mention the importance of the ideal gas temperature scale in expressing temperatures through other scales.
A mass of \(110 \mathrm{~kg}\) is hung from a spring in a local gravitational field where \(g=9.806 \mathrm{~m} / \mathrm{s}^{2}\), and the spring is found to deflect by \(30 \mathrm{~mm}\). If the
Justify the following statement with an example: 'A reversible process proceeds without any driving force'.
A pump delivers water from a well that is \(50 \mathrm{~m}\) deep. Determine the change in potential energy per \(\mathrm{kg}\) of water. Take \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\).
'All spontaneous processes are irreversible'. Explain with a common example.
What are the factors responsible for the irreversibility of a process?
A vacuum gauge mounted on a condenser reads \(0.73 \mathrm{~mm} \mathrm{Hg}\). Determine the absolute pressure in the condenser in \(\mathrm{kPa}\) when the atmospheric pressure is \(101.35
Explain the importance of the demonstration of Joule's experiment in the formulation of the first law of thermodynamics.
The total energy of a typical closed system is given by \(E=25+155 T+0.07 T^{2}\) in Joules. The amount of heat absorbed by the system can be expressed as \(Q=3500+9 T\) in Joules. Estimate the work
The total energy of a typical closed system is given by \(E=50+25 T+0.05 T^{2}\) in Joules. The amount of heat absorbed by the system can be expressed as \(Q=4000+10 T\) in Joules. Estimate the work
Give a proper concept of energy, internal energy, kinetic energy and potential energy.
The latent heat of vaporization of Freon- 11 at \(23.6^{\circ} \mathrm{C}\) and 1 atm is \(5960 \mathrm{~g}\)-cal \(/ \mathrm{g}-\mathrm{mol}\). Calculate \(\Delta U\) and \(\Delta H\) of this
A paddle-wheel is employed in a rigid container for stirring a hot fluid to be cooled. The internal energy of the hot fluid is \(1000 \mathrm{~kJ}\). During the cooling process, the fluid losses
Justify the following statement: "The first law of thermodynamics is nothing but the law of conservation of energy".
In a stirrer-container assembly, the stirrer performs \(3 \mathrm{hp}\) work on the system containing a certain amount of fluid. The heat developed by stirring is \(5000 \mathrm{~kJ} / \mathrm{hr}\)
A stirrer-container assembly contains a certain amount of fluid. The stirrer performs \(3 \mathrm{hp}\) work on the system. The heat developed by stirring is \(4000 \mathrm{~kJ} / \mathrm{h}\) and is
Derive the mathematical expression of the first law of thermodynamics.
A system consisting of a gas confined in a cylinder undergoes a series of processes shown in Fig. 2.11. During the process A-1-B, \(70 \mathrm{~kJ}\) of heat is added while it does 45 \(\mathrm{kJ}\)
A system consisting of a gas confined in a cylinder undergoes a series of processes shown in Fig. 2.4. During the process A-1-B, \(60 \mathrm{~kJ}\) of heat is added while it does \(35 \mathrm{~kJ}\)
A system undergoes a constant pressure process \(1-2\), during which \(100 \mathrm{~kJ}\) of work done on the system and \(50 \mathrm{~kJ}\) of heat as energy is released to the surroundings. Then
What is internal energy? Prove that internal energy is a state function.
A piston-cylinder assembly containing a gas undergoes a process in which the temperature of the system rises from \(100^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\). The heat transmission per
What is the significance of Joule's experiment in finding out the change in internal energy of an ideal gas?
An ideal gas is compressed adiabatically and reversibly in a piston-cylinder assembly from \(30 \mathrm{~L}\) to \(3 \mathrm{~L}\) at \(300 \mathrm{~K}\). Calculate the final temperature, given that
The pressure of a gas is given by \(P=\frac{15}{V}\), where \(P\) is in atmosphere and \(V\) is in litres. If the gas expands from 20 to \(60 \mathrm{~L}\) and undergoes an increase in internal
The pressure of a gas is given by \(P=\frac{10}{V}\), where \(P\) is in atmospheres and \(V\) is in litres. If the gas expands from 10 to \(50 \mathrm{~L}\) and undergoes an increase in internal
Define the term enthalpy. How does it relate to the internal energy?
In an insulated vessel \(1 \mathrm{~kg}\) of water \(\left(C_{V}=4.78 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\right)\) is stirred by a mass of \(40 \mathrm{~kg}\) falling through \(25 \mathrm{~m}\).
What is thermodynamic state and what are state functions?
Prove the following statement: 'For an ideal gas, the internal energy is a function of temperature only'.
A bullet of \(3 \mathrm{~g}\) flying horizontally at \(2 \mathrm{~km} / \mathrm{s}\) strikes a fixed wooden block \((m=6 \mathrm{~kg}\), \(\left.C_{V}=0.14 \mathrm{~kJ} /
\mathrm{~kg}\) of water is vaporized in a container at the constant temperature of \(373 \mathrm{~K}\) and the constant pressure of \(1,01,325.0 \mathrm{~N} / \mathrm{m}^{2}\). The specific volume of
Calculate \(\Delta U, \Delta H, Q\) and \(W\) if \(1 \mathrm{~mol}\) of an organic liquid is converted reversibly into vapour at \(353 \mathrm{~K}\) by supplying heat from external source. The
\(0.52 \mathrm{~kg}\) air is heated reversibly at constant pressure from an initial state of \(37^{\circ} \mathrm{C}\) and \(1 \mathrm{kPa}\) until its volume is doubled. Calculate \(\Delta U, \Delta
State the first law of thermodynamics and mention its importance for a cyclic process.
10 moles of an ideal gas at \(37^{\circ} \mathrm{C}\) are allowed to expand isothermally from an initial pressure of \(15 \mathrm{~atm}\) to a final pressure of \(5 \mathrm{~atm}\) against a constant
One mol of an ideal gas, used as a working substance in a Carnot cycle, operates initially at \(610 \mathrm{~K}\) and \(10^{6} \mathrm{~N} / \mathrm{m}^{2}\) in the compression stage. The gas then
5 moles of an ideal gas was initially at \(315 \mathrm{~K}\) and \(20 \mathrm{~atm}\). The expansion of gas takes place adiabatically when the external pressure is reduced to \(7 \mathrm{~atm}\).
Derive an expression of the work done in a constant-temperature process.
\mathrm{~kg}\) of air at \(50^{\circ} \mathrm{C}\) expands reversibly and adiabatically to 5 times its original volume. The initial pressure of the air mass was \(8 \mathrm{~atm}\). Determine the
Give a brief account of constant-volume and constant-pressure processes.
\mathrm{~mol}\) of an ideal gas was initially at \(293 \mathrm{~K}\) and \(15 \mathrm{~atm}\). The expansion of gas takes place adiabatically when the external pressure is reduced to \(5
In a constant-volume calorimeter, \(1 \mathrm{~mol}\) of trinitrotoluene (TNT) on explosion produces \(3 \mathrm{~mol}\) of \(\mathrm{CO}\) and \(2 \mathrm{~mol}\) of \(\mathrm{N}_{2}\). When
\mathrm{~kg}\) of air is heated from an initial state of \(37^{\circ} \mathrm{C}\) and \(101.33 \mathrm{kPa}\) until its temperature reaches \(237^{\circ} \mathrm{C}\). Calculate \(\Delta U, Q, W\),
\(3 \mathrm{~kg}\) of air at \(45^{\circ} \mathrm{C}\) expands reversibly and adiabatically to 4 times its original volume. The initial pressure of the air mass was \(9 \mathrm{~atm}\). Determine the
Prepare an energy balance for an open system.
What is isothermal expansion? With the help of a neat sketch, substantiate the significance of a porous plug experiment.
In an adiabatic change for an ideal gas, show that the work done in an adiabatic expansion\[ W=\frac{P_{1} V_{1}}{\gamma-1}\left[1-\left(\frac{P_{2}}{P_{1}}\right)^{\frac{\gamma-1}{\gamma}}\right] \]
Show that for an ideal gas the amount of work done by reversible isothermal expansion is always greater than that by irreversible isothermal expansion.
What do you mean by heat capacity and specific heat?
In a frictionless piston-cylinder arrangement, an ideal gas undergoes a compression process from an initial state of 1 bar at 300 K to 10 bars at 300 K. The entire process comprises the following two
Show that for an ideal gas, when volume and enthalpy are separate functions of temperature and pressure\[ C_{P}-C_{V}=\left[V+\left(\frac{\partial H}{\partial T}\right)_{P}\left(\frac{\partial
Prepare an energy balance over an isothermal compression system.
A certain quantity of an ideal gas is contained in a cylinder and occupies a volume of \(1.0 \mathrm{dm}^{3}\) at \(3 \mathrm{~atm}\) pressure. The gas is transferred by different paths to a final
A spherical balloon of 1 m diameter contains a gas at 120 kPa. The gas inside the balloon is heated until the pressure reaches 360 kPa. During heating the pressure of the gas inside the balloon is
1 kmol of argon gas confined in a cylinder undergoes a change from an initial condition of 10 bar and 250 K to a final condition of 1 bar and 300 K. The gas follows the equation PV = RT. Given that
If \(C_{P}=a+b T+C T^{2}\), derive a relation to the isobaric mean heat capacity \(\dot{Q}\).
Hydrogen gas is expanded reversibly and adiabatically from a volume of \(2.12 \mathrm{dm}^{3}\) at a pressure of \(4 \mathrm{~atm}\) and \(32^{\circ} \mathrm{C}\) until the volume is doubled.
Calculate the molar volume of methane at \(672 \mathrm{~K}\) and 12 bar using the following methods:(a) Ideal gas equation of state(b) Van der Waals equation of state, where \(a=0.2303
What are free energy functions? Classify them. Mention the importance of free energy functions in the analysis of thermodynamic processes.
If the internal energy of a substance is considered to be a function of temperature and volume, then show that\[ d U=C_{V} d T+\left(\frac{T \beta}{\alpha}-P\right) d V \]
For an isothermal reversible change of the system\[ -\Delta A_{T}=W_{\max } \]explain the significance of the preceding equation in the light of Helmholtz free energy.
A gas obeys the equation of state \(V=\frac{R T}{P}-\frac{C}{T^{3}}\). Find out the variation of \(C_{P}\) with pressure at constant temperature.
Derive the following relations for a pure substance:(a) \(\left(\frac{\partial H}{\partial T}\right)_{V}=C_{V}+\frac{\beta V}{\alpha}\)(b) \(\left(\frac{\partial H}{\partial P}\right)_{T}=V(1-T
In the study of the phase change process of a pure substance, derive the Clapeyron equation.
Derive an expression to calculate the change in enthalpy and entropy of a real gas undergoing an isothermal compression and obeying the following equation of state:\[ V=\frac{R T}{P}+b-\frac{a}{R T}
Show that for a van der Waals gas\[ \alpha=\frac{V-b}{P V-\frac{a}{V}+\frac{2 a b}{V^{2}}} \quad \text { and } \quad \beta=\frac{R}{P V-\frac{a}{V}+\frac{2 a b}{V^{2}}} \]
Show that \(\left(\frac{\partial C_{P}}{\partial P}\right)_{T}=\frac{2 a}{T^{2}}\) for a gas under isenthalpic condition obeying the equation of state\[ V=\frac{R T}{P}+b-\frac{a}{R T} \]
The inlet and outlet diameters of a conduit are \(10 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) respectively. If the velocity of water flowing through the conduit at the inlet is \(5 \mathrm{~m} /
The inlet and outlet diameters of a pipe are \(15 \mathrm{~cm}\) and \(20 \mathrm{~cm}\) respectively. If the velocity of water flowing through the pipe at the inlet is \(7 \mathrm{~m} /
What are the limitations of the continuity equation?
Water flows through a pipe of \(30 \mathrm{~cm}\) diameter. The flow splits into two parts and passes through pipes of diameters \(25 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) respectively. Find the
Water flowing through a pipe of \(20 \mathrm{~cm}\) diameter. The flow splits into two parts and passes through pipes of diameters \(15 \mathrm{~cm}\) and \(10 \mathrm{~cm}\) respectively. Find the
Prove: 'Bernoulli's equation is a restrictive form of energy equation'.
A pipe, through which water is flowing, has diameters \(30 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) at crosssections 1 and 2 respectively. The discharge velocity of the pipe is \(40 \mathrm{~L} /
A pipe, through which water is flowing, has diameters \(30 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) at cross-sections 1 and 2 respectively. The discharge of the pipe is \(40 \mathrm{~L} / \mathrm{s}\).
What are the assumption made for the establishment of Bernoulli's equation?
A shell and tube heat exchanger is used to cool lubricating oil by water at the rate of \(120 \mathrm{~kg} / \mathrm{min}\). The oil enters the heat exchanger at \(343 \mathrm{~K}\) and leaves at
Air at \(100 \mathrm{kPa}\) and \(320 \mathrm{~K}\) is to be compressed steadily to \(600 \mathrm{kPa}\) and \(430 \mathrm{~K}\) in a reversible compressor. The mass flow rate of the air is \(0.03
Establish the mechanical energy balance equation starting from the law of conservation of energy for a control volume.
A nozzle, through 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 \(523 \mathrm{~K}\),
\(7.5 \quad \mathrm{CO}_{2}\) enters an adiabatic compressor at \(100 \mathrm{kPa}\) and \(250 \mathrm{~K}\) at a rate of \(0.1 \mathrm{~m}^{3} / \mathrm{s}\) and leaves at \(500 \mathrm{kPa} .
Explain the important role of a throttling device for cold production.
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
A shell and tube heat exchanger is used to cool lubricating oil by water at the rate of \(180 \mathrm{~kg} / \mathrm{min}\). The oil enters the heat exchanger at \(353 \mathrm{~K}\) and leaves at
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
With the help of a neat sketch, substantiate the significance of a porous plug experiment.
Steam is desired to cool by water in a condenser. Steam enters the condenser at \(50 \mathrm{kPa}\) and \(50^{\circ} \mathrm{C}\) with a flow rate of \(10 \mathrm{~kg} / \mathrm{min}\) and leaves at
When can heating effect instead of cooling effect be produced by a throttling device?
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