KEY for Unit 8 - Heat and Work in Physical and Chemical
Transformations
Example Problem:
How many Joules of heat are absorbed by 30.0g of water when brought from 35°C to
80°C?
First find ∆t and then calculate q given that the specific heat of water is 4.18 J/g°C.
∆t = tfinal - tinitial = 80°C - 35°C = 45°C
q = 30.0g * 4.18 J/g°C * 45°C
q = 5,643 J
Example Problem:
When 1.0g of NaCl is dissolved in 10.0g of water the calorimeter temperature goes down
from 26.5°C to 23.0°C. How many joules of energy are produced?
0 = qcal + qsolution
qsolution = -mwater * 4.18 J/g°C * ∆t
qsolution = -10.0g * 4.18 J/g°C * -3.5°C
qsolution = +146.3 J
Then the heat of solution can be expressed as a molar quantity by dividing by the moles
of NaCl used.
qsolution = +0.146 kJ/(1.0 g / 58.45 gmol-1) = +8.55 kJmol-1
Example Heat Flow Problem:
A geologist is out in the field collecting rock samples. There may be no firewood
available in the area. He expects to use 50.0 cups of boiling water (for tea, soup, shaving,
etc.) during the trip. He has a portable stove that uses gasoline (octane, C8H18 ) as the
energy source. Given that the stove is 40% efficient in heating the water (initial T = °C),
how much fuel does he have to carry during the trip? Note that gasoline is sold by
volume (gallons) not mass.
Possibly useful information:
1 cup = 8 fl. oz. (exact)
1 fl. oz. = 29.57 cm3
1 gallon = 3.78 L
density of water = 1.00 g/cm3
density of octane = 0.7025 g/cm3
sp. heat of water = 4.18 J/(g deg C)
Heats of formation
water(liq) : - 285.8 kJ/mol
octane(liq) = -250.1 kJ/mol
CO2 = -383.5 kJ/mol [note correction to typo, ∆Hf for CO2 is not -250.1 kJ/mol]
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Answer: First balance a reaction for the combustion of octane and find the change in
enthalpy (∆H) for that reaction.
Next, determine the total amount of heat needed to heat the desired volume of water.
Finally, determine the amount of octane that will need to be combusted to heat the
desired volume of water (recall the stove operates at 40% efficiency).
First: C8H18(l) +
25
/2 O2 (g) Æ 8 CO2 (g) + 9 H2O(l)
∆H = Σ m ∆Hf (prod) - Σ n ∆H f (react)
∆H = 8mole*(-383.5 kJ/mol) + 9mole*(- 285.8 kJ/mol) – 1mole*(-250.1 kJ/mol)
∆H = -5390.1 kJ / mole octane
Second: 50.0 cups of boiling water need to be produced from water at Tinit=20°C
1.00 g
29.57 cm3
find mass of water = (
/cm3)*(
mass of water = 11,828 g = 11.828 kg
/ 1 fl. oz.)*(8 fl. oz./ 1 cup)* 50 cups
find heat needed to raise water from Tinit=20°C to Tfinal=20°C
kJ
heat = m*Cp*∆T = (11.828 kg)*(4.18 /kg °C)*(100°C -20°C)
heat = 3,955 kJ needed to heat the water
Finally: determine the amount of octane needed to produce enough heat to boil the water
accounting for the fact that the stove is 40% efficient.
∆H = -5390.1 kJ / mole octane
heat = 3,955 kJ needed to heat the water but if the stove is only 40% efficient we will
need to produce 9,988 kJ
9,988 kJ needed to heat the water
octane needed =
octane needed = 1.853 mole
/ 5,390.1 kJ / mole octane
volume of octane = (1 gal/3.78 L)*(1 L / 702.5 g octane)*(114.22 g/mol)*1.853 mol
volume of octane = 0.0797 gallon = 10.2 fl oz.
Cirent: Industrial Problem
Cirent Semiconductor is a joint venture between, Lucent Technologies' Microelectronics
Group and Cirrus Logic, Inc.. The facility, located in South Orlando, is undergoing a
$600 million expansion and will be home to more than 600 new engineering and
technical jobs over the next two years. The plant manufactures advanced computer chips
and currently houses more than 1,200 people, including a Bell Labs research and
development group. Construction of a new cleanroom for the manufacture of integrated
circuits on eight-inch silicon wafers is completed and production is expected to begin in
early 1997. Cirent Semiconductor will be the largest manufacturer of semiconductor
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devices in Florida, and as a joint venture, will enhance each company's ability to meet the
worldwide demand for advanced integrated circuits, which are used increasingly in
products such as computing equipment, cellular phones, pagers and other electronic
devices.
Lucent Technologies was created as part of AT&T's restructuring into three separate,
publicly held companies. During the last 16 years, American Telephone and Telegraph
(which included Bell Labs, Western Electric, Long Lines, Network Systems and the
Regional/Local Telephone Companies) divested into AT&T and seven independent
regional operating companies such as BellSouth, Ameritech, Nynex, etc. AT&T acquired
NCR as well as other smaller companies after the divesture. Now AT&T has spun off
Network Systems and AT&T Microelectronics (formerly Western Electric) as Lucent
Technologies. NCR will be spun off by the end of the year. The Microelectronics Group
of Lucent designs and manufactures integrated circuits, optoelectronic components,
power systems, and printed circuit boards for applications in the telecommunications and
computing industries. In addition to such components, Lucent Technologies offers public
and private networks, communications systems and software, and consumer and business
telephone systems. Bell Laboratories is the research and development arm of the new
company.
Headquartered in Fremont, Calif., Cirrus Logic is a leading manufacturer of advanced
integrated circuits that perform multimedia, communications and mass storage functions.
Having captured strong market positions in key sectors of the desktop and portable PC
markets, the company is now extending its core technologies beyond the PC to innovate
software-rich chip solutions for the Interactive Age.
1. In semiconductor processing, silicon tetrachloride has been most studied and has
seen the widest industrial use for growing epitaxial silicon. This is the defect free
layer that is grown on the surface of silicon wafers cut from a grown ingot and
polished. This is the starting layer for all silicon devices. The overall reaction can
be classified as a hydrogen reduction of a gas. This reaction normally is
performed at 1200 deg C in a chemical vapor deposition reactor.
The overall reaction is:
SiCl4 (gas) + 2H2 (gas)
Si (solid) + 4HCl (gas)
four of the reactions that actually occur during the overall process follow:
a. SiCl4 (gas) + H2 (gas)
b. SiHCl3 (gas) + H2 (gas)
c. SiH2Cl2 (gas)
SiHCl3 (gas) + HCl (gas)
SiH2Cl2 (gas) + HCl (gas)
SiCl2 (gas) + H2 (gas)
d. SiCl2 (gas) + H2 (gas)
Si (solid) + 2HCl
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Demonstrate the correct combination of these equations to get the net equation:
1*Rxn(a) SiCl4 (gas) + H2 (gas)
SiHCl3 (gas) + HCl (gas)
1*Rxn(b) SiHCl3 (gas) + H2 (gas)
1*Rxn(c) SiH2Cl2 (gas)
SiCl2 (gas) + H2 (gas)
1*Rxn(d) SiCl2 (gas) + H2 (gas)
SiCl4 (gas) + 2H2 (gas)
o
SiH2Cl2 (gas) + HCl (gas)
Si (solid) + 2HCl
Si (solid) + 4HCl (gas)
The following two problems concern heat produced form exothermic
reactions in an etch system. Fluorine chemistry is very important in the processing
or etching of silicon. We produce the fluorine by a variety of means (which is a
special set of problems, possibly too difficult at this stage of your education). A
problem is the heat generated and how to control it, as it always affects the
wafers. This problem has been greatly simplified (thus it is workable). You may
find the following properties of silicon (see below in answer) invaluable as you
solve the problem, all data may not be necessary - so be careful.
2. The enthalpy of the exothermic reaction:
Si (solid) + 4F (gas)
SiF4 (gas)
is 370 kcal/mole at 25 degC. At what rate is heat being generated when a 200mm
diameter, 0.75mm thick silicon wafer is etched on one surface at a rate of 1
micrometer per minute?
The silicon properties are:
o
o
o
o
o
specific heat = 0.7J/(g degC)
thermal conductivity = 1.5W/(cm degC)
atoms of Si = 5.0 x 1023
density = 2.33 g/cm3
Atomic Weight = 28.09
Find amount of silicon etched per minute then multiply by 370 kcal/mole.
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radius of wafer = 100 mm or 10.0 cm
area of wafer = π (r)2 = π (10.0 cm)2 = 100*π cm2
etch rate in thickness units = 1 µm / minute = 0.0001 cm / min
volume of wafer etched per min = (100*π cm2)*(0.0001 cm/min) = 0.0314 cm3/min
mole Si / min = (mole /28.09 g)*(2.33 g/cm3)*(0.0314 cm3/min) = 2.61x10-3 mol/min
heat generated by rxn = (370 kcal/mole)*(2.61x10-3 mol/min) = 0.964 kcal/min
3. Let's assume that the wafer is thermally isolated during the etching. By how much
will its temperature rise if 5.0 micrometers of silicon is etched away?
5.0 minutes will be required to etch microns . . . so the total heat generated is . . .
total heat generated = 5 minutes*(0.964 kcal/min) = 4.82 kcal
If the silicon is thermally isolated then all the heat will remain in the wafer.
The total wafer mass = volume*density = area*thickness*density
area of wafer = π (r)2 = π (10.0 cm)2 = 100*π cm2
thickness of wafer = 0.75 mm = 0.075 cm
total wafer mass = (100*π cm2)*(0.075 cm)* (2.33 g/cm3) = 54.9 g Si
heat = mass * Cp * ∆T
so ∆T = heat /(mass * Cp ) = 4.82 kcal (4,184 J/kcal) /(54.9 g * 0.7 Jg-1°C-1)
∆T = 525°C
Clearly the wafer gets hot, but it also conducts away some of the heat as it is generated.
The amount of heat that dissipates from the wafer is a bit harder to calculate. The
calculation would involve the use of the thermal conductivity of the Si (given above), but
the real solution to the problem involves differential equations and is beyond the scope of
this course.
4. High energy photons are used to disrupt polymeric bonds or to link bonds to form
a polymer in photoresists. Negative resists become less soluble in developer when
they are exposed to radiation and positive resists become more soluble after
exposure. There are advantages to both types of resists but each is exposed by
using the "i-th" emission line from a mercury vapor lamp. The wavelength is
365nm.
(a) What is the frequency of these light photons? ν = c/λ = 8.22 x 10+14 Hz
(b) What is the energy of a single photon at this wavelength?
E = hν = 5.45x10-19 J . . . . .which corresponds to 328 kJ per mole of photons
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