Woc Ch05-3 Problem Solving and Unit Conversions

8/6/2019 Woc Ch05-3 Problem Solving and Unit Conversions

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Section 5.3

Problem Solving and Unit Conversions

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 toanother

4. To practice using problem solving techniques

5. To define density and its units

Objectives



Section 5.3


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?



Section 5.3



� We can convert from one system of units to another by a

method called dimensional analysis using conversion

factors.

� Unit1 v conversion factor = Unit2

Converting Units of Measurement



Section 5.3



� 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 = 0.394 inches

� Conversion factors are ratios of the two parts of the

equivalence statement that relate the two units.

1 inch or 2.54cm or 0.394 inches or 1 cm .

2.54cm 1 inch 1 cm 0.394 inches

Converting Units of Measurement



Section 5.3



2.85 cm = ? in.

2.85 cm v conversion factor = ? in.

Equivalence statement 2.54 cm = 1 in.

Possible conversion factors

Converting Units of Measure

Does this answer make sense?



Section 5.3


32 Degrees?



Section 5.3


..or 32

Degrees?



Section 5.3


32 Degrees?

.

.

.

.

.

.

.

..

.

. .

.

.

.

.

.. .

.



Section 5.3


B. Temperature Conversions

� There are three commonly used temperature scales,

Fahrenheit, Celsius and Kelvin.



Section 5.3



� 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.

Converting Between the Kelvin and Celsius Scales



Section 5.3



70 oC = ? K

T C + 273 = T K

Converting Between the Kelvin and Celsius Scales

70 + 273 = 343 K



Section 5.3



� Note

Converting Between the Fahrenheit and Celsius Scales

± The different size units

± The different zero points

� To convert between Fahrenheit and Celsius we need to

make 2 adjustments.

ToC = ?



Section 5.3


Convert These Temperatures

200oC to K

-52oC to K

345K to

o

C11K to oC

212oF to oC

32oF to oC

525oF to oC

25oC to oF

-20oC to oF

200

o

F to K



Section 5.3


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



Section 5.3


How to Remember the Density Relationships

D

m

v

Q. Where do

you get your

permit?

A. At the DMV



Section 5.3


Calculate the Missing Quantity:

Mass Volume Density

4.53kg 225 cm3 ? g/cm3

26.3g 25.0 mL ? g/cm3

1.00 lb 500. cm3 ? g/cm3

352 mg 0.000271 L ? g/cm3

? g 45 mL 2.45 g/cm3

1000 g ? mL 10.5 g/cm3

? g 10 L 0.0023 g/mL

1.45 kg ? L 2.67 g/mL

Remember the ³DMV´ 1 lb = 454 g



Section 5.3


C. Density

H2 = 0.084 kg/m3 Is the hydrogen number correct?



Section 5.3


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?

(Egg density demo)

What is the density of water in kg/m3?

Woc Ch05-3 Problem Solving and Unit Conversions

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