Section 5. 3 Problem Solving and Unit Conversions Objectives 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
Section 5. 3 Problem Solving and Unit Conversions 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 Problem Solving and Unit Conversions 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. • Unit 1 conversion factor = Unit 2
Section 5. 3 Problem Solving and Unit Conversions 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. 54 cm 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. 54 cm or 0. 394 inches or 1 cm. 2. 54 cm 1 inch 1 cm 0. 394 inches
Section 5. 3 Problem Solving and Unit Conversions 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 Does this answer make sense?
Section 5. 3 Problem Solving and Unit Conversions A. Tools for Problem Solving 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. Go back and solve the Driving Problem in Canada
Section 5. 3 Problem Solving and Unit Conversions 32 Degrees?
Section 5. 3 Problem Solving and Unit Conversions . . or 32 Degrees?
Section 5. 3 Problem Solving and Unit Conversions. . . . 32 Degrees? . .
Section 5. 3 Problem Solving and Unit Conversions B. Temperature Conversions • There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin.
Section 5. 3 Problem Solving and Unit Conversions 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.
Section 5. 3 Problem Solving and Unit Conversions B. Temperature Conversions Converting Between the Kelvin and Celsius Scales 70 o. C = ? K TC + 273 = TK 70 + 273 = 343 K
Section 5. 3 Problem Solving and Unit Conversions 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. To. C = ?
Section 5. 3 Problem Solving and Unit Conversions Convert These Temperatures 200 o. C to K -52 o. C to K 345 K to o. C 11 K to o. C 212 o. F to o. C 32 o. F to o. C 525 o. F to o. C 25 o. C to o. F -20 o. C to o. F 200 o. F to K
Section 5. 3 Problem Solving and Unit Conversions At what temperature would a Celsius and a Fahrenheit thermometer read the same? To F = To C
Section 5. 3 Problem Solving and Unit Conversions 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 Problem Solving and Unit Conversions How to Remember the Density Relationships Q. Where do you get your permit? A. At the DMV m D v
Section 5. 3 Problem Solving and Unit Conversions Calculate the Missing Quantity: Mass Volume 4530 g 225 cm 3 ? g/cm 3 26. 3 g 25. 0 m. L ? g/cm 3 1. 00 lb 500. cm 3 ? g/cm 3 0. 352 g 0. 000271 L ? g/cm 3 ? g 45 cm 3 2. 45 g/cm 3 1000 g ? m. L 10. 5 g/cm 3 ? g 10 L 0. 0023 g/m. L 1. 45 kg ? L 2. 67 g/m. L Remember the “DMV” Density 1 lb = 454 g
Section 5. 3 Problem Solving and Unit Conversions C. Density H 2 = 0. 084 kg/m 3 Is the hydrogen number correct?
Section 5. 3 Problem Solving and Unit Conversions 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/m. L or 1 g/cm 3 How much does 150 m. L of water weigh? What is the density of water in kg/m 3? (Egg density demo)
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