Introduction The Scientific Method and Measurement
Defining How We Look At The Universe Observation: seeing an event or process in nature we wish to explain Hypothesis: a tentative explanation based on previous knowledge (experience) Theory: allows prediction of the outcome of future tests of the hypothesis
Developing a Theory Test the Hypothesis: set up experiments designed to tell you if the hypothesis is correct Repeating tests: after many different tests, assume the hypothesis is correct Try to Predict: See if the hypothesis allows prediction for new circumstances
Measurement Precision is indicated by significant figures Arithmetic rules for precision differ for addition/subtraction and multiplication/division
Addition and Subtraction When combining numbers, round or truncate the answer based on the data with the fewest decimal places 10.6871 cm +1.42 cm 12.1071 = 12.11 cm
Multiplying and Dividing When multiplying or dividing, the answer is expressed with the same number of significant figures as the data with the least number of significant figures. 12.35 units X 2.12512 units = 26.245232 units 4 significant figures 26.25 units
Significant Figures Trapped Zeros are significant: 709 10001 1.029 Zeros to the right of digits and decimals are significant 8.0 5.700 810. Zeros to the left are not significant 0.0070
Determining the Number of Significant Figures PROBLEM: For each of the following quantities, underline the zeros that are significant figures(sf), and determine the number of significant figures in each quantity. For (d) to (f) express each in exponential notation first. (a) 0.0030 L (b) 0.1044 g (c) 53.069 ml (d) 0.00004715 m (e) 57,600. s (f) 0.0000007160 cm 3 PLAN: Determine the number of sf by counting digits and paying attention to the placement of zeros. SOLUTION: (a) 0.0030 L 2sf (b) 0.1044 g 4sf (c) 53.069 ml 5sf (d) 0.00004715 m (e) 57,600. s (f) 0.0000007160 cm 3 (d) 4.715x10-5 m 4sf (e) 5.7600x10 4 s 5sf (f) 7.160x10-7 cm 3 4sf
Rules for Significant Figures in Answers 1. For addition and subtraction. The answer has the same number of decimal places as there are in the measurement with the fewest decimal places. Example: adding two volumes 83.5 ml + 23.28 ml 106.78 ml = 106.8 ml Example: subtracting two volumes 865.9 ml - 2.8121 ml 863.0879 ml = 863.1 ml
Rules for Rounding Off Numbers 1. If the digit removed is more than 5, the preceding number increases by 1. 5.379 rounds to 5.38 if three significant figures are retained and to 5.4 if two significant figures are retained. 2. If the digit removed is less than 5, the preceding number is unchanged. 0.2413 rounds to 0.241 if three significant figures are retained and to 0.24 if two significant figures are retained. 3.If the digit removed is 5, the preceding number increases by 1 if it is odd and remains unchanged if it is even. 17.75 rounds to 17.8, but 17.65 rounds to 17.6. If the 5 is followed only by zeros, rule 3 is followed; if the 5 is followed by nonzeros, rule 1 is followed: 17.6500 rounds to 17.6, but 17.6513 rounds to 17.7 4. Be sure to carry two or more additional significant figures through a multistep calculation and round off only the final answer.
Significant Figures and Rounding PROBLEM: Perform the following calculations and round the answer to the correct number of significant figures. (a) 16.3521 cm 2-1.448 cm 2 7.085 cm (b) 1 g 4.80x10 4 mg 1000 mg 11.55 cm 3 PLAN: In (a) we subtract before we divide; for (b) we are using an exact number. SOLUTION: 16.3521 cm 2-1.448 cm (a) 2 = 7.085 cm 14.904 cm 2 = 2.104 cm 2 7.085 cm (b) 4.80x10 4 mg 11.55 cm 3 1 g 1000 mg = 48.0 g 11.55 cm 3 = 4.16 g/ cm 3
Rules for Significant Figures in Answers 2. For multiplication and division. The number with the least certainty limits the certainty of the result. Therefore, the answer contains the same number of significant figures as there are in the measurement with the fewest significant figures. Multiply the following numbers: 9.2 cm x 6.8 cm x 0.3744 cm = 23.4225 cm 3 = 23 cm 3
Scientific Notation Standard notation : N X 10 x where N is 1 to 9 and x =+/- integers 1.0 x 10 2 25 x 10 3 is NOT standard (2.5 x 10 4 is ).025 x 10 1 is NOT standard ( 2.5 x 10-1 is )
Shorthand Number Notation 2000.0 x 10 0 = 2000.0 2.0 x 10 3 = 2000.0 The exponent (x) is the number of decimal places moved to get standard notation from data
Counting places Move decimal place until it fits standard notation: 0.00055 00005.5 5.5 x 10-4 moved decimal four places to the right 3000.0 3.0 x 10 3 moved decimal three places to the left
Rules for Scientific Notation Moving the decimal to the right produces a negative exponent, equal to the number of places moved Moving the decimal to the left produces a positive exponent equal to the number of places moved
Unit Dimensional Analysis Mathematical origin of units and conversion between units Factor-Label (dimensional analysis) method Consistency in measures
Converting to New Units 36 hrs x 60 min. x 60 sec. = 129600 sec. 1 hour 1 minute Conversion factors are unit definitions
Converting Distance Units 55 miles per hour to Kilometers per second 55 mi x 5,280 ft x 12 in x 2.54 cm x 1 m x hr mi ft in 100cm 1 Km x 1 hr x 1 min = 0.0245872 Km/s 1000 m 60 min 60 sec = 2.5 x 10-2 Km /s
Unit Conversion S 5x10 What is the value of S in cm per second? 3 furlongs fortnight Conversion Factor: number with 2 different units of measure Solution requires convenient placement of conversion factors: S 5x10 3 furlongs fortnight x 1 mile 8 furlong 5280 feet x mile 12inches x foot x 2.54cm inch 1fortnight x 14days x 1day 24hours 1hour x 3600sec 83.15cm sec
Standard Units of Measure
Common SI-English conversion factors Quantity SI Unit SI Equivalent English Equivalent English to SI Equivalent Length 1 kilometer(km) 1000(10 3 )m 0.62miles(mi) 1 mi = 1.61km Volume 1 meter(m) 100(10 2 )m 1.094yards(yd) 1000(10 3 )mm 39.37inches(in) 1 centimeter(cm) 0.01(10-2 )m 0.3937in 1 kilometer(km) 1000(10 3 )m 0.62mi 1 cubic meter(m 3 ) 1,000,000(10 6 ) cubic centimeters 1 cubic decimeter (dm 3 ) 1 cubic centimeter (cm 3 ) 1000cm 3 35.2cubic feet (ft 3 ) 0.2642 gallon (gal) 1.057 quarts (qt) 1 yd = 0.9144m 1 foot (ft) = 0.3048m 1 in = 2.54cm (exactly!) 1 mi. = 5,280 ft. 1 ft 3 = 0.0283m 3 1 gal = 3.785 dm 3 1 qt = 0.9464 dm 3 0.001 dm 3 0.0338 fluid ounce 1 qt = 946.4 cm 3 1 fluid ounce = 29.6 cm 3 Mass 1 kilogram (kg) 1000 grams 2,205 pounds (lb) 1 gram (g) 1000 milligrams 0.03527 ounce(oz) 1 (lb) = 0.4536 kg 1 lb = 453.6 g 1 ounce = 28.35 g
The Freezing and Boiling Points of Water
Conversion Factors o C = 5/9 ( o F-32) o F= 9/5 o C+32 Kelvin Temperature units: K= o C +273.15
At Boiling: o C = 5/9 (212 o 32) = 100 o C o F=9/5 * 100 o C + 32 = 212 O F
Common Decimal Prefixes Used with SI Units Prefix Prefix Symbol Number Word Exponential Notation tera T 1,000,000,000,000 trillion 10 12 giga G 1,000,000,000 billion 10 9 mega M 1,000,000 million 10 6 kilo k 1,000 thousand 10 3 hecto h 100 hundred 10 2 deka da 10 ten 10 1 ----- ---- 1 one 10 0 deci d 0.1 tenth 10-1 centi c 0.01 hundredth 10-2 milli m 0.001 thousandth 10-3 micro 0.000001 millionth 10-6 nano n 0.000000001 billionth 10-9 pico p 0.000000000001 trillionth 10-12 femto f 0.000000000000001 quadrillionth 10-15
Densities of Some Common Substances Density = mass/volume Substance Physical State Density (g/cm 3 ) Hydrogen Gas 0.000089 Oxygen Gas 0.0014 Grain alcohol Liquid 0. 789 Water Liquid 1.000 Table salt Solid 2.16 Aluminum Solid 2.70 Lead Solid 11.3 Gold Solid 19.3
Specific Gravity When the density of a substance is compared to the density of water(1.00g/ml), the units divide out. The resulting unit less number allows simple evaluation. The value of the specific gravity for any substance is equal to it s density (g/ml).
Energy Kinetic Energy- matter that is in motion has an energy associated with it that is related to the mass and the speed: K.E.= ½ mv 2
Potential Energy Stored energy Position provides potential for motion Energy stored in molecular substances such as fuel Nuclear emission used to heat steam that move turbines Results in kinetic energy if released!
Conservation of Matter and Energy Energy can neither be created nor destroyed Matter can be converted to energy The total energy of the universe is constant
Heat Energy Particles that make up matter can absorb energy and transfer energy in the form of heat. Associated with the absorption of heat energy is an increase in temperature. Heat energy causes the particles that make up matter to jiggle around more. (have more kinetic energy).
Measuring Heat The amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius is the SPECIFIC HEAT: We usually measure the temperature increase of water 1 Calorie = 4.184 Joules Cal/g. o C
Thermochemistry The specific heat can be used to measure the amount of heat in a substance Temperature changes often occur with chemical reactions Amount of heat energy=sh x mass x (T 2 -T 1 ) where T 2 is the final temp and T 1 is the starting temp of the material.