PROBLEMS
23.1 Which is an example of an exothennic phase change? (1) liquid to solid; (2) 1iquid to gas; (3) solid to liquid; (4) solid to gas.
23.2 Explain the difference between latent heat and sensible heat, and compare their relative magnitudes.
23.3 Does the heat of vaporization depend on temperature? temperature?
23.4 Heat is added to a substance at a constant rate and the temperature of the substanceremains the same. This substance is (1) solid melting at its melting point; (2) solidbelow its melting point; (3) Jiquid above its freezing point; (4) liquid freezing at its freezing point.
23.5 The graph below shows a pure substance which is heated by a constant source of heat
supply.
Use the numbers in the diagram to denote the following stages: (a) being wanned as a solid (b) being warmed as a liquid (c) being warmed as a gas (d) changing from a solid to a liquid (e) changing from a liquid to a gas Also, what is its boiling temperature? The freezing temperature?
23.6 Show that the heat (enthalpy) of fusion is essentially identical to the internal energy
of fusion.
23.7 The vapor pressure of zinc in the range 600 to 985°C is given by the equation
Use the numbers in the diagram to denote the following stages: (a) being wanned as a solid (b) being warmed as a liquid (c) being warmed as a gas (d) changing from a solid to a liquid (e) changing from a liquid to a gas Also, what is its boiling temperature? The freezing temperature?
23.6 Show that the heat (enthalpy) of fusion is essentially identical to the internal energy
of fusion.
23.7 The vapor pressure of zinc in the range 600 to 985°C is given by the equation
where P = vapor pressure, mm Hg
=
temperature, K . T Estimate the latent heat of vaporization of zinc at its normal boiling point of 907°C.
23.8 The vapor pressure of phenylhydrazine has been found to be (from 25° to 240°C):
where p'" is in atm and T is in 0℃. What is the heat of vaporization of phenylhydrazine in Btullb mol at 200°F? Use the Clausius-Clapeyron equation.
23.9 Use the Clausius-Clapeyron equation to solve the following problem. One hundred
g mol of benzene (C6HcJ are placed in a 100 L vessel at 35°C. What is the vapor pressure of benzene at 35°C? Data: At 320 K the vapor pressure of benzene is measured and found to be 0.211 atm and the physical property data at 320 K (from a hand· book) are:
23.10 Estimate ∆H for n-heptane at its normal boiling point point given: Tb = 98.43°C, Tc=
540.2 K, Pc = 27 atm. Use Chen's Equation. Calculate the % error in this value
compared to the tabulated value of 31.69 kJ/g mol.
23.11 Determine the heat of vaporization of benzene at its normal boiling point by using
Riedel's equation (Equation 23.6).
23.12 Cumene, C9H12 (isopropyl benzene) has a normal boiling point of 152.4 °C. Estimate
the heat of vaporization of cumene at 100°C using the Watson equation.
23.13 Estimate each of the following: (a) Heat of sublimation of ice
(b) Heat of vaporization of water (c) Heat of fusion of ice
(d) The triple point of water
Using the equations in section 23.1.
23.14 Some measurements of the thermodynamic properties of n-butane gave the
following values at 30℃ : Specific gravity of saturated liquid = 0.564 g/cm3 Specific gravity of saturated vapor (air=1.00 at 0 ℃ and 1 atm) = 6.50 Latent heat of vaporization = 356.5 J/g
The vapor pressure as a function of temperature (T in K) was found to be
As an embryonic engineer you are asked to evaluate the above data and determine whether or not the values are consistent.
23.15 An oil, with a density less than one, and containing small quantities of water, was
being heated in a vessel in order to drive off the water vapour. prior to carrying out a reaction, The water and oil were immiscible. The heating medium was a heat transfer fluid at 250 cC, the heat being transmitted via concentric coils the fluid being in the coils. During the initial stages the manhole was partly open and, after heating had been applied for some time the operator noticed that he had omitted to start the agitator. On doing this large quantities of the oil were ejected with considerable force through the open manhole and ejection continued until only approximately one quarter of theoriginal contents were left in the reactor. What was the cause of this accident?
23.16 Estimate the heat capacity of gaseous isobutance at 1000 K and 200 mm Hg by using the Kothari-Doraiswamy relation
from the following experimental data at 200 mm Hg:
The experimental value is 227.6; what is the percentage error in the estimate?
23.17 Heat capacity data for gaseous NH3 are listed below:
Fit an equation of the form C p = a + bT + cT 2 and an equation of the form C p = a + bT + cT2 + dT3. Compare your results with the heat capacity equation for NH3 gas in Appendix E. Hint: Use Polymath.
23.18 Experimental values calculated for the heat capacity of ammonia from -40 to
1200℃ are:
Fit the data by least squares for the following two functions:
Hint: Use Polymath.
23.19 Experimental values of the heat capacity C p have been determined in the laboratory as follows; fit a second-order polynomial in temperature to the data (C p = (J + bT + cT(2):
(The data are for carbon dioxide.)
23.20 An equation for the heat capacity of acetone vapor is C p = 71.96 + 20.lO X 10-2 T - 12.78 X 10-5 12
where C p is in J/(g mol)(℃) and T is in mol)(℉) and T is in ℉.
+ 34.76 X 10-9 P
℃. Convert the equation so that C p is in Btu/(1b
23.21 Your assistant has developed the following equation to represent the heat capacity of air (with C p in cal/(g mol) (K) and Tin K): C p = 6.39 + 1.76 X 10-3 T - 0.26 X 10 6 T2
a) b)
p but with the temperature expressed in ℃. Derive an equation giving C
Derive an equation giving C p in terms of Btu per pound per degree Fahrenheit with the temperature being expressed in degrees Fahrenheit.
23.22 An equation for the heat capacity of carbon (solid) was given in an article as
C p = 1.2 + 0.0050 T - 0.0000021 T 2
where C p is in Btu/(1b)(°F) and T is in ℃℉. The calculated value of the enthalpy for C at l000℉ is 1510 Btu/1b. What is the reference temperature for the calculation of the enthalp y of carbon?
23.23 You have been asked to review the calculations of
~
assistant with respect to the calculation
of the internal energy of CO2, The assistant looked up the enthalpy of CO2 at 600 kPa and 283K (16,660 kJ/gmol ), and then calculated on the basis of 1 g mol.
Is this calculation correct?
23.24 The enthalpy of Al2O3 can be represented by the equation
where ∆H is in J/g mol and T is in K. Detennine an equation for the heat capacity of Al2O3
as a function of temperature.
23.25 G. E. Moore reported an equation for the high temperature enthalpy of manganese diox ide
as:
Is this equation valid?
23.26 General Electric Co. has developed an advanced fuel-cell battery that will supply the primary power needed during orbit by space capsules. The peak load delivered by the battery will be just under 2 kW. The facility will be assembled from ion-exchange membrane cells, in which the membranes are sheets of a tough, undisclosed plastic. The fuels supplied to the cells will be hydrogen and oxygen. Though fed in the gaseous state during battery operation, these two elements will be stored as liquids, to conserve space.
The equipment is inherently reliable because it is simple, and it achieves 60% thermal efficiency under normal load. Also, the battery will yield a by-product that is highly valuable in space-flight-a pint of pure drinkable water for each kilowatt-hour of operation. If the O2 and the H2 are stored as saturated liquids at their nonnal boiling point. what is the enthalpy change per g mol of O 2 between the liquid storage tank and the state at which the O2 enters the fuel cell (1.5 atrn, 27°C).
23.27 Two gram moles of nitrogen are heated from 50°C to 250°C in a cylinder. What is ∆H for the process? The heat capacity equation is
C p = 27.32 + 0.6226 X 10-2 T - 0.0950 X 10-5 T 2 where T is in kelvin and C p is in J/(g mol)(℃).
23.28 Calculate the change in enthalpy for 5 kg mol of CO which is cooled from 927°C to 327°C.
23.29 Hydrogen sulfide is heated from 77℃ to 227°C. What is the enthalpy change due to the heating?
23.30 What is the enthalpy change for acetylene when heated from 37.SoC to 93.3°C?
23.31 You are asked to calculate the electric power required (in kWh) to heat all of an aluminum wire (positioned in a vacuum similar to a light bulb filament) from 25°C to 660°C (liquid) to be used in a vapor deposition appararus. The melting point of Al is 660°C. The wire is 2.5 mm in diameter and has a length of 5.5 cm. (The vapor deposition occurs at temperatures in the vicinity of 900°C).
Data: For AI, C p = 20.0 + 0.0135 T where T is in K and C p is in J/(g mol)(OC). The ∆Hfusion = 10,670 J/(g mol)(℃) at 660°C. The density of Al is 19.35 g/cm3.
23.32 Ca1culate the enthalpy change (in J/kg mol) that takes place in raising the temperature of 1 kg mol of the following gas mixture from 50°C to 550°C.
23.33 In a proposed molten-iron coal gasification process (Chemical Engineering, July 51985: 17), pulverized coal of up to 3 mm size is blown into a molten iron bath, and oxygen and steam are blown in from the bottom of the vessel. Materials such as lime for settling the slag, or steam for batch cooling and hydrogen generation. can be injected at the same time. The sulfur in the coal'reacts with lime to fonn calcium sulfide, which dissolves into the slag. The process operates at atmospheric pressure and 1400 to 1500°C. Under these conditions. coal volatiles escape immediately and are cracked. The carbon conversion rate is said to be above 98%, and
the gas is typically 65 to 70% CO, 25 to 35% H2• and less than 2% CO 2' Sulfur content of the gas is less than 20 ppm. Assume that the product gas is 68% CO, 30% H 2 and 2% CO2, and calculate the enthalpy change that occurs on the cooling of 1000 m 3 at 1400°C and I atm of gaseous product from 1400°C to 25°C and 1 atm. Use the table for the enthalpies of the combustion gases.
23.34 Determine the enthalpy change when one gram mole of SO 2 gas is cooled from 538°C to 101°C at 1 atmosphere pressure. Data: .
Boiling point:
-SoC
Melting point:
-75.5°C
Latent heat of vaporization:
24,940 J/g mol
Latent heat of fusion:
7,401 JIg mol
p of liquid SO2 as: 1.28 J/(g mol)(℃) Use the average C p of solid SO2 as: Use the average C
0.958 J/(g mol)(℃)
Use the C p of gaseous SO2 from Appendix E.
23.35 Calculate the enthalpy change (in joules) that occurs when 1 kg of benzene vapor at 150°C and 100 kPa condenses to a solid at -20.0°C and 100 kPa.
23.36 One hundred kg of HCl gas are cooled from 300 to 150°C at 1 atm pressure. Calculate ∆H and ∆U in kJ. The heat capacity equation found in a handbook is -9 3 -3 -6 2 p = 7.24 - 1.76 X 10 T + 3.07 X 10 T - 10 T C
23.37 Use the tables for the heat capacities of the combustion gases in the Appendix to compute the enthalpy change (in Btu) that takes place when a mixture of 6.00 lb mol of gaseous H 20 and 4.00 lb mol of CO2 is heated from 60oP to 600oP.
23.38 Use of the steam tables: a. What is the enthalpy change needed to change 3 Ib of liquid water at 32℉ to steam at 1 atm and 300℉? b. What is the enthalpy change needed to heal 3 lb of water from 60 psia and 32°F to steam at 1 atm and 300°F? c. What is tbe enthalpy change needed to heat 1 Ib of water at 60 psia and 40°F to steam at 300℉ and 60 psia?
d. What is the enthalpy change needed. to change 1 lb of a water-steam mixture of 60% quality to one of 80% quality if the mixture is at 300°F? e. Calculate the ∆H value for an isobaric (constant pressure) change of steam from 120 psia and 500℉ to saturated liquid. f.
Repeat part (e) for an isothermal change to saturated liquid.
g. Does an enthalpy change from saturated vapor at 450oP to 21 and 1 psia represent an enthalpy increase or decrease? A volume increase or decrease? h. In what state is water at 40 psia and 261.24°F? At 70 psia and 302℉? At 70 psia and 304℉? i.
A 2.5-ft3 tank of water at 160 psia and 363.5 ℉ has how many cubic feet of liquid water it? Assume that you start with 1 Ib of H. Could it contain S Ib of H 2O under these conditions?
j.
What is the volume change when 2 lb of H 2O at 1000 psia and 20℉ expands to 245 psia
and 460℉? k. Ten pounds of wet steam 100 psi a has an enthalpy of 9000 Btu. Find quality of the wet steam.
23.39 Use the steam ,tables To calculate the enthalpy change (in joules) of 2 kg mol of steam when heated from 400 K and 100 kPa to 900 K and 100 kPa. Repeat using the table in the text for the enthalpies of combustion gases. Repeat using the heat capacity for steam. Compare your answers. Which is most accurate?
23.40 A closed vessel contains steam at 1000.0 psia in a to-1 vapor volume-to-liquid volume ratio. What the steam quality?
23.41 What is the enthalpy change in British thermal units when 1 gal of water is heated from 60°F to 1150oP and 240 psig.
23.42 What is the enthalpy change that takes place when 3 kg of water at 101.3 kPa and 300 K are vaporized to 15.000 kPa and 800K?
23.43 Wet steam flows in a pipe at a pressure of 700 kPa. To check the quality, the wet steam is expanded adiabatically to a pressure of 100 kPa in a separate pipe. A thermo-couple inserted into the pipe indicates the expanded steam has a temperature of 25°C. What was the quality of the wet steam in the pipe prior to expansion?
23.44 If 30 m3 of combustion products at 1l00 K of the following composition: 6.2% O2, 1.0%
H20, 12.3% CO2, and the balance N2 are cooled at atmospheric pressure from 1100 K to 300 K, what is the enthalpy change in kJ? Use the table for the enthalpies of the
combustion gases.
23.45 Equal quantities by weight of water at +50°C and of ice at -40°C are mixed together. What
will be the final temperature of the mixture?
23.46 A chart for carbon dioxide (see Appendix) shows that the enthalpy of saturated CO2 liquid is zero at -40°F. Can this be true? Explain your answer.
23.47 Use the CO2 chart for the following calculations. 1. Four pounds of CO2 are heated from saturated liquid at 20"P to 600 psia and 180°F. a) What is the specific volume of the CO2 at the final state? b) Is the CO2 in the final state gas, liquid. solid, or a mixture of two or three phases? 2. The 4 Ib of CO2 is then cooled at 600 psia until the specific volume is 0.07 ft3llb. a) What is the temperature of the final state? b) Is the CO2 in the final state gas, liquid, solid, or a mixture of two or three phases?
23.48 Calculate the internal energy (actually 1l0) of CO2 at 40℉ and 40 psia in Btu/lb. You can use the CO2 chart in the Appendix of the book for the data.
23.49 Calculate the enthalpy change in heating 1 g mole of CO2 from 50° to 100°C at I atm. Do
this problem by three different methods: 1. Use the heat capacity equation from the Appendix; 2. Use the CO2 chart in the Appendix; 3. Use the Table of Combustion Gases.
23.50 Use the chart for n-butane to calculate the enthalpy change for 10 Ib of butane going from
a volume of 2.5 ft3 at 3600P to saturated liquid at 10 atm.
23.51 A propane gas tank is fined. closed and attached to a barbecue grill. After standing some time what is the state of the propane inside the tank? What are the temperature and pressure inside the tank? After using 80% of the propane in the tank, what is the pressure inside the tank after it reaches equilibrium.
