9/26/2011
Section 5.3
Section 5.3
Problem Solving and Unit Conversions
Problem Solving and Unit Conversions
Objectives
A. Tools for Problem Solving
1. To learn how dimensional analysis can be used to solve
problems
2. To learn the three temperature scales
3. To learn to convert from one temperature scale to
another
4. To practice using problem solving techniques
5. To define density and its units
• Be systematic
• Ask yourself these questions
– Where do we want to go?
– What do we know?
– How do we get there?
– Does it make sense?
Section 5.3
Section 5.3
Problem Solving and Unit Conversions
Problem Solving and Unit Conversions
A. Tools for Problem Solving
A. Tools for Problem Solving
Converting Units of Measurement
Converting Units of Measurement
• We can convert from one system of units to another by a
method called dimensional analysis using conversion
factors.
• Unit1 conversion factor = Unit2
• Conversion factors are built from an equivalence
statement which shows the relationship between the
units in different systems.
• Conversion factors are ratios of the two parts of the
equivalence statement that relate the two units.
Section 5.3
Section 5.3
Problem Solving and Unit Conversions
Problem Solving and Unit Conversions
A. Tools for Problem Solving
A. Tools for Problem Solving
Converting Units of Measure
2.85 cm = ? in.
2.85 cm
conversion factor = ? in.
Equivalence statement
2.54 cm = 1 in.
Possible conversion factors
Tools for Converting from One Unit to Another
Step 1 Find an equivalence statement that relates the 2
units.
Step 2 Choose the conversion factor by looking at the
direction of the required change (cancel the
unwanted units).
Step 3 Multiply the original quantity by the conversion
factor.
Step 4 Make sure you have the correct number of
significant figures.
Does this answer make sense?
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9/26/2011
Section 5.3
Section 5.3
Problem Solving and Unit Conversions
Problem Solving and Unit Conversions
B. Temperature Conversions
B. Temperature Conversions
• There are three commonly used temperature scales,
Fahrenheit, Celsius and Kelvin.
Converting Between the Kelvin and Celsius Scales
• Note that
– The temperature unit is the same size.
– The zero points are different.
• To convert from Celsius to Kelvin we need to adjust for
the difference in zero points.
Section 5.3
Section 5.3
Problem Solving and Unit Conversions
Problem Solving and Unit Conversions
B. Temperature Conversions
B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales
70. oC = ? K
TC + 273 = TK
70. + 273 = 343 K
Converting Between the Fahrenheit and Celsius Scales
• Note
– The different size units
– The different zero points
• To convert between Fahrenheit and Celsius we need to
make 2 adjustments.
Section 5.3
Section 5.3
Problem Solving and Unit Conversions
Problem Solving and Unit Conversions
C. Density
Calculating with Density
• Density is the amount of matter present in a given
volume of substance.
• From the definition of density, it can be derived:
• Mass = Density x volume
• Volume = mass/Density
• Given a mass of a piece of aluminum is 10.50 g and its
volume is 3.89 mL , what is its density?
• 10.50 g / 3.89 mL = 2.70 g/mL = 2.70 g/cm 3
• Given a piece of aluminum has a mass of 22.48 g, what
is its mass?
• 22.48 g x 1 cm3/2.70 g = 8.33 cm3
• Given a different piece of aluminum has a volume of
24.0 cm3, what is its mass?
• 24.0 cm3 x 2.70 g/cm3 = 64.8 g
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9/26/2011
Section 5.3
Problem Solving and Unit Conversions
C. Density
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