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engineering
introduction to chemical engineering thermodynamics

Introduction To Chemical Engineering Thermodynamics 2nd Edition HALDER - Solutions

Explain the importance and application of Peng-Robinson equation of state.
Calculate the pressure of \(1.0 \mathrm{kmol}\) of methane occupying a volume of \(0.9 \mathrm{~m}^{3}\) in a vessel at a constant temperature of \(533 \mathrm{~K}\) by using(a) ideal gas equation,(b) van der Waals equation of state when \(a=0.4233 \mathrm{Nm}^{4} / \mathrm{mol}^{2}\) and \(b=3.73
Name some proposed model equations of state for real gases.
What is compressibility factor? Explain its necessity for showing the deviation from ideal gas behaviour for real gases.
The virial equation for ethane is given by \(P V=R T+B P\). At \(0^{\circ} \mathrm{C}, B=-0.1814 \mathrm{~L} / \mathrm{mol}\). Calculate the volume of \(1 \mathrm{~mol}\) of ethane at \(10 \mathrm{~atm}\), given that van der Waals constant \(a=5.489 \mathrm{~atm}-\mathrm{L} / \mathrm{mol}\).
Discuss the importance of generalized compressibility chart.
Determine the compressibility factor of steam at \(627 \mathrm{~K}\) and \(200 \mathrm{kPa}\) using(a) van der Waals equation and(b) Redlich-Kwong equation of state when \(P_{\mathrm{C}}=123.2\) bar and \(T_{\mathrm{C}}=398 \mathrm{~K}\).
State the law of corresponding state and show that the gases are obeying the law by plotting a graph of \(Z\) versus \(P_{\mathrm{R}}\).
A steel cylinder of \(6 \mathrm{~L}\) capacity contains \(500 \mathrm{~g}\) of nitrogen. Calculate the temperature to which the cylinder may be heated without the pressure exceeding \(50 \mathrm{~atm}\), given that the compressibility factor, \(Z=0.945\).
Write a short note on superheated vapour.
Using the Peng-Robinson equation of state, calculate the volume of a gas contained in a vessel of capacity \(0.8 \mathrm{~m}^{3}\) at \(574 \mathrm{~K}\) and 18 bar. \(T_{\mathrm{C}}=190.6 \mathrm{~K}, P_{\mathrm{C}}=45.99 \mathrm{bar}\), \(V_{\mathrm{C}}=98.6 \mathrm{~cm}^{3} / \mathrm{mol},
What is virial equation of state?
Calculate the acentric factor for ethanol. The vapour pressure of methanol can be estimated from the following equation:\[ \log _{10} P^{\mathrm{Sat}}=8.1122-\frac{1592.864}{t+226.184} \]where \(P^{\text {Sat }}\) is in \(\mathrm{mm} \mathrm{Hg}\) and \(t\) is in \({ }^{\circ} \mathrm{C}\). The
Write informatory notes on Redlich-Kwong-Soave equation of state Benedict-Webb-Rubin equation of state.
Calculate the second virial coefficients for benzene at \(350 \mathrm{~K}\) and \(8 \mathrm{~atm}\), given that \(T_{\mathrm{C}}=560.3 \mathrm{~K}, P_{\mathrm{C}}=47.89 \mathrm{bar}\), and \(\omega=0.2112\).
How do you explain the significance of virial coefficients?
The Berthelot equation of state is given by\[ \left(P+\frac{a}{T V^{2}}\right)(V-b)=R T \]where \(a\) and \(b\) are constants. Show that \(a=\frac{27 R^{2} T_{\mathrm{C}}^{3}}{64 P_{\mathrm{C}}}, b=\frac{R T_{\mathrm{C}}}{8 P_{\mathrm{C}}}, Z_{\mathrm{C}}=\frac{3}{8}\) from the knowledge of point
What is acentric factor?
Explain the role of thermo-chemistry in the design and analysis of chemical processes and their relevant equipments.
State Hess's law of constant heat summation with a suitable example. How can it be explained from the thermodynamic point of view?
The heat of formation of ammonia and hydrogen fluoride gas are \(-46.1 \mathrm{~kJ}\) and -271.2 \(\mathrm{kJ}\) respectively. Estimate the heat of the reaction\[ 2 \mathrm{NH}_{3}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g})=\mathrm{N}_{2}(\mathrm{~g})+6 \mathrm{HF}(\mathrm{g}) \]
Consider the following heat changes in the oxidation of magnesium and iron.Reaction involved:(i) \(\mathrm{Mg}+\frac{1}{2} \mathrm{O}_{2}=\mathrm{MgO} \quad \Delta H=-602.06 \mathrm{~kJ} / \mathrm{mol}\)(ii) \(2 \mathrm{Fe}+\frac{3}{2} \mathrm{O}_{2}=\mathrm{Fe}_{2} \mathrm{O}_{3} \quad \Delta
What is the usefulness of Hess's law of constant heat summation?
The latent heat of formation of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})=-5800 \mathrm{cal}\) at \(500 \mathrm{~K}\). What will be the heat of formation at \(1000 \mathrm{~K}\) ? We are given that\[ \begin{aligned} C_{P_{\mathrm{H}_{2}}} & =6.94-0.2 \times 10^{-3} T \\ C_{P_{\mathrm{O}_{2}}} &
Calculate the standard heat of formation of \(\mathrm{CH}_{4}\), given the following experimental results at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) :(a) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}\) (g) \(\rightarrow 2 \mathrm{H}_{2} \mathrm{O}\) (l)\[ \Delta H_{1}=-241.8 \times
Write informatory notes on the following:(a) Heat of formation(b) Heat of reaction(c) Heat of combustion(d) Standard heat of reaction(e) Standard heat of formation
For the reaction\[ \mathrm{CO}+\frac{1}{2} \mathrm{O}_{2}=\mathrm{O}_{2} \quad \Delta H=-67650 \text { cal at } 25^{\circ} \mathrm{C} \]find out \(\Delta H\) of the process at \(100^{\circ} \mathrm{C}\), given that molal heat capacities \(C_{P_{\mathrm{CO}}}=6.97\), \(C_{P_{\mathrm{CO}_{2}}}=8.97\)
Calculate the values of \(\Delta H_{298}^{0}\) for the following reactions in the transformation of glucose in an organism:\[ \begin{align*} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s}) & =2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})+2 \mathrm{CO}_{2}(\mathrm{~g}) \tag{A}\\
How do you estimate the heat of reaction at unknown temperature with respect to the heat of reaction of the substance at known temperature?
The heat of combustion of \(n\)-heptane (1) at constant volume and at \(25^{\circ} \mathrm{C}\) is \(-1150 \mathrm{kcal} / \mathrm{mol}\). Calculate the \(\Delta H_{f}^{0}\) for \(n\)-heptane, given that \(\Delta H_{f_{\mathrm{CO}_{2}(\mathrm{~g})}}=-94 \mathrm{kcal} / \mathrm{mol}, \Delta
On the basis of the data and the chemical reactions given in the following lines, find the heat of formation of \(\mathrm{ZnSO}_{4}\) from its constituent elements.\[ \begin{align*} \mathrm{Zn}+\mathrm{S} & =\mathrm{ZnS} & \Delta H & =-44.0 \mathrm{kcal} / \mathrm{kmol} \tag{A}\\ 2 \mathrm{ZnS}+3
Define the term adiabatic flame temperature. How can it be determined?
Calculate the theoretical flame temperature for \(\mathrm{CO}\) when burned with \(100 \%\) excess air while both the reactants are at \(373 \mathrm{~K}\). The heat capacities of \(\mathrm{CO}, \mathrm{O}_{2}, \mathrm{~N}_{2}\) and \(\mathrm{CO}_{2}\) are \(29.33 \mathrm{~J} /
Calculate the heat of formation of ammonia. The heats of combustion of ammonia and hydrogen are -90.6 and \(-68.3 \mathrm{kcal}\) respectively.
What is the importance of theoretical flame temperature?
Calculate the standard heat of the following gaseous reaction at \(773 \mathrm{~K}\) :\[ \mathrm{CO}_{2}+4 \mathrm{H}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{CH}_{4} \quad \Delta H_{298}=-164.987 \mathrm{~kJ} \]The specific heat of the components are represented by \(C_{P}=a+b T+C
The heat of combustion of acetylene is \(-310600 \mathrm{cal}\). If the gas is heated from room temperature \(\left(25^{\circ} \mathrm{C}\right)\) to a higher temperature. Determine the maximum attainable temperature.
What is excess air? What role does it play for the complete combustion of a fuel?
Determine the standard heat of the following reaction at \(298 \mathrm{~K}\) :(a) \(\mathrm{CaC}_{2}\) (s) \(+\mathrm{H}_{2} \mathrm{O}\) (l) \(\rightarrow \mathrm{C}_{2} \mathrm{H}_{2}\) (g) \(+\mathrm{CaO}\) (s)(b) \(4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4
Calculate the theoretical temperature of combustion of ethane with \(25 \%\) excess air. The average specific heats in \(\mathrm{kJ} / \mathrm{kg}-\mathrm{K}\) may be taken as follows:\[ \begin{aligned} \mathrm{CO}_{2} & =54.56 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K} \\ \mathrm{O}_{2} & =35.20
What is the difference between excess air and theoretical air?
Calculate the standard enthalpy change of combustion at \(298.15 \mathrm{~K}\) for \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l})\) if \(\mathrm{H}_{2} \mathrm{O}\) is in the gaseous state.
The latent heat of fusion of ice at \(0^{\circ} \mathrm{C}\) is \(1440 \mathrm{cal} / \mathrm{mol}\) and the heat capacity of ice \(/ \mathrm{mole}\) is \(6.7 \mathrm{cal}\). Calculate the latent heat of ice at \(-20^{\circ} \mathrm{C}\).
Name the factors responsible for incomplete combustion even if excess air is supplied to the fuel.
The heat of formation of ammonia from its constituent elements is \(11030 \mathrm{cal} / \mathrm{mol}\) at \(300 \mathrm{~K}\). What will be its heat of formation at \(1273 \mathrm{~K}\) ?We are given that \(C_{\mathrm{P}_{2}}=6.94-0.2 \times 10^{-3} T, C_{P_{\mathrm{N}_{2}}}=6.45+1.4 \times
A student pours chloroform into the palm of his hand. As the liquid evaporates, his hands feels cold. Is the process of evaporation of chloroform exothermic or endothermic?
A sample of dry flue gas has the following composition by volume: \(\mathrm{CO}_{2}-\) \(13.4 \%, \mathrm{~N}_{2}-80.5 \%\) and \(\mathrm{O}_{2}-6.1 \%\). Calculate the excess air supplied. Assume that the fuel contains no nitrogen. The oxygen and nitrogen must have come from air.
What is the difference between complete combustion and theoretical combustion?
The heat of combustion of cyclopropane \(\left(\mathrm{CH}_{2}\right)_{3}\) is \(-2090 \mathrm{~kJ} / \mathrm{mol}\). The heat of formation of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are -393.5 and \(-285.8 \mathrm{~kJ} / \mathrm{mol}\), respectively. Calculate(a) the heat of
The chemical equation for the water gas reaction between \(\mathrm{CO}\) and steam is\[ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \]Determine the enthalpy of reaction at \(25^{\circ} \mathrm{C}\) and \(1
Sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) burns at \(25^{\circ} \mathrm{C}\) to form \(\mathrm{CO}_{2}\) gas and liquid \(\mathrm{H}_{2} \mathrm{O}\), releasing \(5,640,000\) \(\mathrm{kJ} / \mathrm{kmol}\) of heat according to the equation\[ \mathrm{C}_{12}
Propane gas at room temperature is burned with enough air so that combustion is complete and gases leave the burner at \(1400 \mathrm{~K}\). The combustion gas is then mixed with sufficient air so that the resulting gas mixture for drying is at \(400 \mathrm{~K}\). How many moles of gas are
Calculate the theoretical temperature of combustion of ethane with \(25 \%\) excess air. The average specific heats in \(\mathrm{kJ} / \mathrm{kg}-\mathrm{K}\) may be taken as follows: \(\mathrm{CO}_{2}=1.24, \mathrm{O}_{2}=1.10\), Steam \(=2.41, \mathrm{~N}_{2}=1.19\). The combustion reaction for
A sample of coal has \(80 \% \mathrm{C}, 0.5 \% \mathrm{H}_{2}, 0.5 \% \mathrm{~S}\), and \(14.5 \%\) ash. Calculate the theoretical quantity of air necessary for the combustion of \(1 \mathrm{~kg}\) of coal. Find the composition of the flue gas by weight and by volume if \(25 \%\) excess air is
Calculate the theoretical flame temperature when hydrogen burns with \(400 \%\) excess air at \(1 \mathrm{~atm}\). The reactant enters at \(100^{\circ} \mathrm{C}\). The reaction involved is\[ \mathrm{H}_{2}+1 / 2 \mathrm{O}_{2}=\mathrm{H}_{2} \mathrm{O} \]
A heat engine is working between a source at \(550^{\circ} \mathrm{C}\) and a sink at \(27^{\circ} \mathrm{C}\). What is the efficiency of the heat engine?
Explain the importance of the first law of thermodynamics. Does the first law give any information about the direction of a process?
A Carnot cycle operates between \(800^{\circ} \mathrm{C}\) and \(150^{\circ} \mathrm{C}\). Determine the efficiency of the cycle, the heat released, and the work output if \(100 \mathrm{~kJ}\) heat enters the cycle.
A reversible heat engine receives the heat from a high-temperature source at \(810 \mathrm{~K}\) and release the same to a low-temperature sink at \(300 \mathrm{~K}\). Determine(a) the thermal efficiency of the heat engine;(b) the efficiency of the engine if the higher temperature is increased to
What are the limitations of the first law of thermodynamics?
An inventor claims to have developed an engine of thermal efficiency \(92 \%\). Check the validity of his claim.
A Carnot engine absorbs heat to the tune of \(585 \mathrm{~kJ} / \mathrm{cycle}\) from a hot reservoir at \(650^{\circ} \mathrm{C}\) and discards heat to a cold reservoir at \(30^{\circ} \mathrm{C}\). Then(a) What is the theoretical efficiency of the Carnot engine?(b) What amount would be released
State and explain the second law of thermodynamics.
An inventor claims to have developed a heat pump with a COP of 4.5. It maintains the cold space at \(255 \mathrm{~K}\). The temperature of the environment is \(305 \mathrm{~K}\). Check the validity of his claim.
It is desired to produce a \(1 \mathrm{~kg}\) ice block from water in a freezer box of a refrigerator at \(273 \mathrm{~K}\) while the temperature of the environment is \(295 \mathrm{~K}\). Given that the latent heat of fusion of ice at \(273 \mathrm{~K}\) is \(335 \mathrm{~kJ} / \mathrm{kg}\),
Explain the Kelvin-Planck and Clausius statements.
A heat engine absorbs \(250 \mathrm{~kJ}\) of heat from a source at \(310 \mathrm{~K}\). The heat engine produces a work to the tune of \(65 \mathrm{~kJ}\), discarding \(110 \mathrm{~kJ}\) of heat to a thermal reservoir at \(312 \mathrm{~K}\) and \(80 \mathrm{~kJ}\) of heat to another reservoir at
A Carnot engine working between a high-temperature source at \(373 \mathrm{~K}\) and a low-temperature sink at \(275 \mathrm{~K}\) receives \(50 \mathrm{~kJ}\) of heat from a high-temperature region. Determine(i) the minimum work required(ii) the efficiency(iii) the amount of heat released.
Prove the equivalence of the Kelvin-Planck and Clausius statements.
An inventor claims to have developed a heat engine that receives \(7000 \mathrm{~J} / \mathrm{s}\) of heat from a source at \(400^{\circ} \mathrm{C}\). The power output of the engine is \(5 \mathrm{hp}\). The temperature of the surroundings is \(24^{\circ} \mathrm{C}\). It can be treated as a sink
Justify: "The violation of the Kelvin-Planck statement is nothing but the violation of the Clausius statement".
Determine the change in entropy when \(200 \mathrm{~g}\) of ice at \(0^{\circ} \mathrm{C}\) is converted into water at the same temperature, given that latent heat of ice \(=80 \mathrm{cal} / \mathrm{g}\).
Calculate the change in entropy for the conversion of \(1 \mathrm{~mol}\) of ice to liquid at \(273 \mathrm{~K}\) and \(1 \mathrm{~atm}\). The latent heat of fusion is \(6500 \mathrm{~J} / \mathrm{mol}\).
What is a heat engine? Calculate its thermal efficiency.
Calculate the entropy change when \(96 \mathrm{~g}\) of methane is heated from \(35^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) at constant volume. Assume \(C_{V}=1.735 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\).
Calculate the change in entropy when 5 moles of an ideal gas expands from a volume of \(5 \mathrm{~L}\) to \(50 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\).
What are the differences between a heat pump and a refrigerator?
\(7 \mathrm{~mol}\) of an ideal gas \(\left(C_{V}=5 \mathrm{cal}\right)\) was initially at \(30^{\circ} \mathrm{C}\) and \(2 \mathrm{~atm}\). The gas was transferred to the state when the temperature is \(110^{\circ} \mathrm{C}\) and pressure \(12 \mathrm{~atm}\). Determine the change in entropy of
Calculate \(\Delta S\) when \(8 \mathrm{~mol}\) of an ideal gas are heated from a temperature of 350 \(\mathrm{K}\) to a temperature of \(700 \mathrm{~K}\) at constant pressure. Assume that \(C_{P}=\frac{5}{2} R\).
What are the common characteristics of a heat engine?
\(5.105 \mathrm{~mol}\) of an ideal gas is expanded from a temperature of \(300 \mathrm{~K}\) at 3 bars to \(400 \mathrm{~K}\) at 12 bars. Assume that \(C_{P}=26.73 \mathrm{~kJ} / \mathrm{mole}-\mathrm{K}\).
What would be the change in entropy when \(2 \mathrm{~kg}\) of air is heated from \(30^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) at constant pressure? Assume \(C_{P}=1.005 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\).
Comment on the statement: "Heat cannot be easily converted into work".
Calculate the increase in entropy when \(2.8 \mathrm{~L}\) of oxygen are mixed with \(19.6 \mathrm{~L}\) of hydrogen at N.T.P.
Calculate the entropy of \(1 \mathrm{kmol}\) of air containing \(21 \%\) oxygen and \(79 \%\) nitrogen by volume. These are at the same temperature and pressure.
What is the basic difference in working principle between a heat pump and a heat engine?
5 kilograms of helium undergoes a constant-volume change from \(317 \mathrm{~K}\) to \(572 \mathrm{~K}\). Determine the entropy change. Assume specific heat, \(C_{V}=3.115 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\).
An ideal gas mixture contains 5.6 L of oxygen and \(16.8 \mathrm{~L}\) of hydrogen at N.T.P. Calculate the increase in entropy.
Explain the working principle of the Carnot cycle with the help of a \(P-V\) diagram.
A process is carried out at constant pressure. It is found that the entropy change is 0.832 \(\mathrm{kJ} / \mathrm{kg}-\mathrm{K}\). If \(C_{P}=0.846 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\) and the upper temperature of the process is \(315^{\circ} \mathrm{C}\), then determine the lower temperature
What would be the change in entropy when \(80 \mathrm{~g}\) of argon is heated from \(300 \mathrm{~K}\) to \(500 \mathrm{~K}\) at constant volume. Assume specific heat \(C_{V}=0.3122 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\).
Why can the thermal efficiency of a heat engine never be \(100 \%\) ?
Find the change in entropy of \(\mathrm{H}_{2}\) when it is heated from \(157^{\circ} \mathrm{C}\) to \(923^{\circ} \mathrm{C}\). The molar specific heat of \(\mathrm{H}_{2}\) is given by \(C_{P}=6.94-0.2 \times 10^{-3} T\).
A process is carried out at constant volume. It is found that the entropy change is \(1.0 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\). If \(C_{V}=0.918 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\) and the lower temperature of the process is \(18^{\circ} \mathrm{C}\), then determine the upper temperature of
Is it possible to achieve a reversible heat engine in practice?
A \(30 \mathrm{~kg}\) block of steel casting at \(635 \mathrm{~K}\) is quenched in \(135 \mathrm{~kg}\) oil at \(283 \mathrm{~K}\). If there are no heat losses, determine the change in entropy. Assume that the specific heat of steel is \(0.72 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\) and that of oil
Estimate the change in entropy if \(5 \mathrm{~kg}\) of water at \(350 \mathrm{~K}\) is mixed adiabatically with \(20 \mathrm{~kg}\) of water at \(250 \mathrm{~K}\). Assume the specific heat of water is \(4.2 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}\).
What is entropy? Give an example.
An iron block weighing \(15 \mathrm{~kg}\) at a temperature of \(450^{\circ} \mathrm{C}\) is in a well-insulated container having \(120 \mathrm{~kg}\) of water at \(5^{\circ} \mathrm{C}\). Determine the change in entropy of(a) the iron block,(b) the water and(c) the total process. Assume that the
\(5.1612 \mathrm{~g}\) of a metal is heated from \(294 \mathrm{~K}\) to \(574 \mathrm{~K}\) in a constant-pressure process. The melting point of metal is \(505 \mathrm{~K}\). We are given that\[\begin{aligned} \text { Latent heat of fusion of the metal } & =14.5 \mathrm{cal} / \mathrm{g} \\ \text {

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