1. Objectives
To learn how dimensional analysis can be used to solve problems
To learn the three temperature scales
To learn to convert from one temperature scale to another
To practice using problem solving techniques
To define density and its units

2. A. Tools for Problem Solving
I am driving in Canada. I have a journey of 120 km and I need to estimate how many liters of gas to buy. I know my car fuel mileage is 24 miles per gallon. (1 mile is 1.6 km, 1 gallon is 3.79 liters)
Be systematic
Ask yourself these questions
What do we know to start with?
Where do we want to go?
How do we get there?
Does it make sense?

3. A. Tools for Problem Solving
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

4. A. Tools for Problem Solving
Converting Units of Measurement
Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems.
1 inch = 2.54cm or 1 cm = inches
Conversion factors are ratios of the two parts of the equivalence statement that relate the two units.
1 inch or 2.54cm or inches or 1 cm .
2.54cm inch 1 cm inches

5. A. Tools for Problem Solving
Converting Units of Measure
2.85 cm = ? in cm  conversion factor = ? in. Equivalence statement cm = 1 in. Possible conversion factors
Does this answer make sense?

6. A. Tools for Problem Solving
Tools for Converting from One Unit to Another
Step 1 Find an equivalence statement that relates the 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.
Go back and solve the Driving Problem in Canada

7. 32 Degrees?

8. ..or 32 Degrees?

9. . . . . . . . . . . . . . . . . . .
32 Degrees? . .

10. B. Temperature Conversions
There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin.

11. B. Temperature Conversions
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.

12. B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales
70 oC = ? K
TC = TK
= 343 K

13. B. Temperature Conversions
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.
ToC = ?

14. Convert These Temperatures
200oC to K -52oC to K 345K to oC 11K to oC 212oF to oC 32oF to oC 525oF to oC 25oC to oF -20oC to oF 200oF to K

15. At what temperature would a Celsius and a Fahrenheit thermometer read the same?
ToF = ToC

16. C. Density
Density is the amount of matter present in a given volume of substance.
Write down all the statements relating the three properties D, M and V

17. How to Remember the Density Relationships
Q. Where do you get your permit?
A. At the DMV D m v

18. Calculate the Missing Quantity:
Mass
Volume
Density
4530 g
225 cm3
? g/cm3
26.3g
25.0 mL
1.00 lb
500. cm3
0.352 g L
? g
45 cm3
2.45 g/cm3
1000 g
? mL
10.5 g/cm3
10 L
g/mL
1.45 kg
? L
2.67 g/mL
Remember the “DMV” 1 lb = 454 g

19. C. Density
H2 = kg/m3 Is the hydrogen number correct?

20. One gram of water has a volume of 1 milliliter
Density of Water
One gram of water has a volume of 1 milliliter
The density of water is……?
D = M/V
Density of water = 1 g/mL or 1g/cm3
How much does 150 mL of water weigh?
What is the density of water in kg/m3?
(Egg density demo)