Heat Problems

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Heat Problems
2
Converting Kelvin and CelsiusTemperatures

• K C 273
• C K - 273
• 300 C __________K
• 473 K __________ C

3
Chapter 2 Using Conversion Factors

• A conversion factor is a ratio derived from the
  equality of two different measurement units.
• For example
• 1 foot 12 inches
• 4 quarters 1 dollar
• 1 ton 2000 pounds

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Slide 2 Using Conversion Factors

• These equalities can be set-up or expressed as
  ratios or fractions.
• The unit is written with the numerical value when
  the equality is expressed as a ratio.
• For example

1 mile 5280 feet
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Slide 3 Using Conversion Factors

• Any equality can be expressed as a conversion
  factor fraction.
• When converting numbers using conversion factors,
  the problem is solved by multiplying the
  conversion factor times the unit to be converted.
• When like units are on the numerator (top) and
  denominator (bottom) they cancel.
• The unit that is left is the unit that goes with
  the number.

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Example Conversion Factor Problem

• How many feet are in 2.75 miles? How many inches
  are in 2.75 miles?
• Conversion factors
• 1 mile 5280 feet 1 foot 12 inches
• 2.75 miles _______feet

Which factor when multiplied times 2.75 miles
will give us feet as answer?
Conversion factor fractions 1 mile
5280 feet 5280 feet 1 mile
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Example Conversion Factor Problem

• 5280 feet
• 1 mile

2.75 miles 1
X
Perform the math operation
5280 feet 1 mile
2.75 miles 1
X
14 520 feet

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Conversion Factor Problem 2A

• How many seconds are in 28 days?
• Conversion factors needed
• 1 minute 60 seconds
• 1 hour 60 minutes
• 1 day 24 hours

What needs to be solved? 28 days ______seconds
X
X
X
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Conversion Factor Problem 2B

• How many seconds are in 28 days?

1. Cancel units 2. Do top operations 3. Do
bottom operations 4. Divide and place unit with
number.
2 419 200 seconds
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Conversion Factor Problem 2c

• How pounds are there in 100 kg?

Conversion factor 1 kilograms 2.2 pound
Setup 100 kg x 2.2 lbs 1
1 kg
Setup 100 x 2.2 lbs 220
lbs 1 1
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Conversion Factor Problem 2d

• How kilograms are there in 100 lbs?

Conversion factor 1 kilograms 2.2 pound
Setup 100 lbs x 1 kg 1
2.2 lbs
100 x 1 kg 45.45 kg 1
2.2
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Significant Figure Video

• 6 minute Video on Significant Figures

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Significant figures or digits

• Every measurement has an error it it due to the
  inaccuracy and imprecision of the measurement
  tool.
• The last place of measurement is called the
  uncertain figure or digit, because it is
  estimated.
• DefinitionSignificant figures in a measurement
  consists of all the digits known with certainty
  plus one final digit which is uncertain or
  estimated.

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Examples of significant figures

• 100.6 grams
• 100 is certain while .6 is uncertain
• 22.7 mL
• 22 is certain while .7 is
  uncertain
• 20.25 o C
• 20.2 are certain while .05 is uncertain

• Zero can be certain or uncertain digits or
  figures.
• There are rules to determine if the zero is
  significant or is to be ignored.

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Rules for determining of Significant Zeros
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Examples for determining the number Significant
Zeros
How many significant figures are in the following
numbers?
125.6 g
4 significant figures
72 000 cm
2 significant figures
0.0012540 L
5 significant figures
40. m
2 significant figures
0.0000007 g
1 significant figures
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Rounding numbers
When rounding numbers, the rules are only
different if the last digit is a 5 and is not
followed by a nonzero digit. The ODD/EVEN rule is
then used.
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Example problemsRounding numbers
Round the following numbers to the number of
significant figures that are indicated
Number Significant figures Answer
45.2351 g
3 significant digits
45.2 g
5.2352 L
3 significant digits
5.24 L
0.2348 m
2 significant digits
0.23 m
145.235 g
5 significant digits
145.24 g
145.225 g
5 significant digits
145.22 g
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Link to Problems

• Chemistry Website

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Math operations and significant figures
1. When adding or subtracting decimals, the
answer must always have the same number of digits
to the right of the decimal point as there are in
the measurement having the fewest digits to the
right of the decimal point. 2. For
multiplication or division, the answer can have
no more significant figures than are in the
measurement with the fewest significant figures.
Add the numbers below and round to the
appropriate number of significant figures needed.
12.05 m 1235.256 m 1247.306
m Answer 1247.31 m
1.2 g 12.256 g 13.456 g Answer
13.5 g
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Math operations and significant figures
1. When adding or subtracting decimals, the
answer must always have the same number of digits
to the right of the decimal point as there are in
the measurement having the fewest digits to the
right of the decimal point. 2. For
multiplication or division, the answer can have
no more significant figures than are in the
measurement with the fewest significant figures.
Multiply the numbers below and round to the
appropriate number of significant figures needed.
2.153 m x 3.0 m 6.459
m2 Answer 6.5 m2
2.0045 cm2 x 5.57 cm 11.1465065
cm3 Answer 11.1 cm3
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Scientific Notation

• In scientific notation, numbers are written in
  the form
• M x 10n
• where
• M a number greater than 1 but less than 10.
• n whole number for the power of ten.
• 2.75 x 102 or 9.74 x 10-5

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Scientific Notation Rules

• 1. Determine M by moving the decimal in the
  original number to the left or right so that only
  one nonzero digit remains to the left of the
  decimal point.
• 2. Determine n by counting the number of decimal
  places you move the decimal.
• 3. If you moved the decimal to the left, n is a
  positive number.
• 2c. If you moved the decimal to the right, n is a
  negative number.

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Scientific Notation examples

• Convert the following numbers to scientific
  notation

Number Places and direction
Answer
12 500 m
4 places left
1.25 x 104 m
0.0375 g
2 places right
3.75 x 10-2 g
0.00075 L
4 places right
7.5 x 10-4 L
125 000 000 sec
8 places left
1.25 x 108 sec
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Adding and subtracting numbers using Scientific
notation

• When adding or subtracting numbers in scientific
  notation, the operation can only be done if both
  numbers have the same power of ten.
• If they do NOT have the same power of ten, select
  one of the numbers and move the decimal place
  until it is in the same power of ten as the other
  number.
• Then perform the operation.

1.205 x 102 m 2.595 x 102 m
3.800 x 102 m
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Example problems Adding and subtracting numbers
Can these numbers be added together? NO
1.205 x 103 m 2.55 x 102 m

Select one of the numbers and change the power of
ten to match the other number. 2.55 x 102
m 0.255 x 103 m
1.205 x 103 m 0.255 x 103 m
1.460 x 103 m
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Multiplying and dividing numbers using Scientific
notation

• When multiplying or dividing numbers in
  scientific notation, the following rules are
  used
• Multiplying
• The M factors are multiplied together, and the
  powers of ten are added together.
• Dividing
• The M factors are divided, and the powers of ten
  are subtracted from each other.

(2.5 x 102) ( 2.0 x 102 ) 2.5
x 2.0 5.0 and 10 2 2 10 4 5.0 x
10 4
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Example problems Multiplying and dividing numbers
(1.2 x 103) (1.2 x 105) 1.2 x 1.2 1.44 10
35 108 1.44 x 108 1.4 x 108
(2.75 x 103) (2.00 x 10-5) 2.75 x 2.00
5.50 10 3(-5) 10-2 5.50 x 10-2

• When an exponent is negative on one of the
  numbers, subtract the numbers.
• The sign of the exponent is determined by which
  number is larger.
• If both exponents are negative add these together
  and keep the negative exponent.

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Example problems Multiplying and dividing numbers
(8.00 x 105) (2.00 x 102) 8/2
4.00 10 5-2 103 4.00 x 103
(5.0 x 103) (2.00 x 10-5) 5.0/2.00
2.50 10 3-(-5) 108 2.5 x 10 8

• Change the sign of the exponent in the
  denominator and add the numbers together.
• When an exponent is negative and in the
  denominator, change the sign of the exponent to
  positve and add the numbers together.

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Example problems Multiplying and dividing numbers
(9.00 x 102) (3.00 x 10-5) 9/3
3.00 10 2-(-5) 107 3.00 x 107
(6.0 x 10 -3) (3.00 x 10-5) 6.0/3.00
2.0 10 -3-(-5) 102 2.0 x 10 2
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Math relationships in Chemistry

• Direct proportions
• Two quantities are expressed as a ratio which
  gives a constant, k values
• m/v k or x/y k
• Graph is a straight line
• Inverse proportions
• Two quantities are expressed as a product which
  gives a constant, k values
• D V k or x y k
• Graph is a hyperbola

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Density a direct relationship
Density is an intrinsic physical property that
has a linear and direct proportionality. Graphing
volume versus mass shows this relationship.
33
Pressure and volume of a gas a inverse
relationship

• A graph of volume versus pressure shows a
  non-linear inverse relationship.
• This curve is called a hyperbola.

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Final Thoughts on Measurement

• Precision
• Reproducibility
• Check by repeating measurements
• Poor precision results from poor technique

• Accuracy
• Correctness
• Check by using a different method
• Poor accuracy results from procedural or
  equipment flaws

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Review for Test

• Accuracy- exactness or closeness to a true or
  accepted value
• Liter- metric base unit for measuring volume
• Precision- the repeatability of a set of
  measurements
• Meter- metric base unit for measuring length
• Centi- metric prefix that means 0.01 or 1/100 or
  10-2
• Milli- metric prefix that means 0.001 or 1/1000
  or 10-3
• SI metric units- agreed metric units that are
  used internationally for measurement

36
Review for Test

• Gram- metric base unit for measuring the amount
  of mass
• kilo- metric prefix that means 1000 or 103
• Volume- the amount of space an object
• Density- the amount of matter in a given space,
  g/cc
• Calorie- the amount of heat needed to raise one
  gram of water by 1 degree Celsius
• Temperature- the average kinetic energy of
  particles of matter a measure of hot and cold
• Heat- the total kinetic energy of particles of
  matter that depends on the mass, change of
  temperature and the type of material

37
Review for Test

• Joule- metric SI unit for measuring heat energy
  where 4.184 J equals 1 calorie
• Kelvin- the SI unit for measuring temperature
  and is based on the kinetic energy content of the
  material
• Variable- a quantity that can be measured or
  calculated
• Direct proportion- a math relationship where
  variables are a ratio and have a constant value.
  (k x/y)
• Inverse proportion- a math relationship where
  variables are a product and have a constant
  value. (k x y)
• Specific heat- the amount of heat needed to raise
  the temperature of one gram of a material by 1
  degree Celsius
• Uncertainity- in measurement it is the last digit
  or figure in significant figures that is measured
  and is estimated.
• Significant figures- in measurement it is all the
  digits in a measurement that are certain and one
  final digit that is uncertain and estimated

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Review Problems

• Convert the following numbers to the proper
  metric units.
• 37.5 mm 0.0375 m
• 1975 mL 1.975 L
• 0.365 m 36.5 cm
• 518.5 g 0.5185 kg
• Convert the following temperatures
• 150 degrees C 423 degrees K
• 573 degrees K 300 degrees C

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Review Problems

• Determine the number of significant figures and
  uncertainty in each of the following numbers
• 235. 5 g SF 4 uncertain digit
  last 5
• 0.01087m SF 4 uncertain digit
  7__

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Review problems
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Review problems
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Review problems
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Review problems

• DENSITY PROBLEMA piece of metal has a mass of
  11.38 grams and has a volume of 1.09 cubic
  centimeter
  
  Common densities (in grams
  per cubic centimeter) Gold - 19.32
  Silver -10.50 Iron - 7.87
  Lead- 11.35
• 
  
  
• 1. What is the density of this metal?
• 2. What is this metal made of? Justify your
  answer

44
Review problems
HEAT PROBLEM Solve the following HEAT problem
please show the formula used, and the set-up of
the problem.

Liquid water
has a specific heat of 4.184 J/(gC). If 100
grams of water is heated from 25 degrees C to 85
degrees C. What is the heat energy (in Joules)
needed to heat this water to this temperature?