Units. Units. conversion factors and units

Transcription

1 Units units are like apples and oranges any number of 1 inch any number! kilograms things with different types of units cannot be equated or compared 1 Units always write every quantity with its associated unit always include units in your calculations - you can do the same kind of operations on units as you can with numbers cm cm = cm 2 cm + cm = cm cm cm = 1 - using units as a guide to problem solving is called dimensional analysis 2 conversion factors and units converting one unit into another often involves ratios called conversion factors conversion factors come from equations 1 inch = 2.54 cm can give two factors divide both sides by 1 inch or divide both sides by 2.54 cm 1 = 2.54cm 1.0in = 1 in 2.54 cm 1 multiplying by either factor is equivalent to multiplying by 1 3 1

2 using conversion factors tip 1: select conversion factors so that the cancels and is replaced by the new desired unit new unit = new unit conversion factor equivalent to multiplying by 1 4 Example: Convert pounds to grams look at equations you have involving pounds and grams 1 lb = grams gives 2 conversion factors pick the conversion factor that will cancel the and has new unit on top quantity in g lb = 136 g 1.0 lb conversion factor cancels quantity in new unit 1.0 lb g g 1.0 lb tip: equations like this are read to mean 1 pound exactly (infinite SF) is g (5 SF) conversion factor has 5 SF Example: Convert 1.76 yd to centimeters look at equations you have involving yards and cm 1 yd = m 1 m = 100 cm yards can be converted to meters then meters converted to centimeters yd m cm 1m 100 cm 1.79 yd = 161cm yd 1m quantity in conversion factors quantity in new unit 2

3 Example: Convert 125 decimeters into meters. 1 meter = 1 meter 1 decimeter = 1 x 10-1 meter you will have this table for the exam gives 2 possible conversion factors 1 x 10-1 meters 1 decimeter 1 decimeter 1 x 10-1 meters 125 decimeters 1 x 10 x -1 meters 1 decimeter conversion factor = 12.5 meters new units 7 Example: Convert 235 nanometers into micrometers. 1 meter = 1 meter tip 2: When converting between units with prefixes use two conversion factors: one to go to the un-prefixed unit and one to go to the new prefixed unit. e.g. in this case nanometers meters micrometers 1 meter = 1 meter 1 nanometer = 1 x 10-9 meter 1 micrometer = 1 x 10-6 meter gives 2 possible conversion factors gives 2 possible conversion factors 1 x 10-9 meters 1 nanometer 1 nanometer 1 x 10-9 meters 1 x 10-6 meters 1 micrometer 1 micrometer 1 x 10-6 meters 235 nanometers x 1 x 10-9 meters 1 micrometer x 1 nanometer 1 x 10-6 meters conversion factors = micrometers 8 Derived Units units built up from base units are called derived units can be multiplied or divided - per means division of units derived unit 1) all formulas for area involve two length dimensions multiplied meter * meter area rectangle =l*w area circle = πr 2 area triangle = ½b*h meter 2 or m 2 2) units of velocity miles per hour miles hour 3) pressure unit pounds per square inch pounds inch 2 9 3

4 Example: Convert 2.11 yard 3 to meters yard 3 x 3 1 meter yard tip 3: conversion factors for units of area or volume can be derived by writing down the conversion factor for the base unit of length and squaring or cubing it 2.11 yard 3 x 1 3 meter yard yard 3 x 1 meter 3 = 1.61 meter yard 3 or 1.61 m 3 10 understanding conversion factors for area/volume area = 1 meter squared 1 decimeter (deci = 10-1 ) or 1 m 2 1 decimeter area = 1 decimeter squared or 1 dm 2 1 meter 1 meter even though a decimeter is 1/10 the length of a meter it would require 100 square decimeters to cover 1 m 2 1 decimeter = 10-1 meter 1 dm 2 = 10-2 m 2 or 100 dm 2 = 1 m 2 11 Converting base units within a derived unit any part of a derived unit can be converted as if it was a base unit alone the SI unit of energy is the derived units called the Joule. 1 Joule = 1 kg*m2 sec 2 Example: Convert joules into units of g*m 2 /sec 2. kg*m 1000 g kg 2 x = 251 g*m g 2 sec 2 1 kg sec 2 units of Joules conversion factor for kg to g new derived units has grams instead of kg it is as if we just converted kg into grams 12 4

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6 Temperature Scales temperature reflects the random motion of matter at the microscopic level at higher temperatures motion is faster most matter expands as it gets warmer and shrinks as it cools 16 Thermometers based upon the expansion of matter as it is warmed calibrated using reference points like boiling water, or ice water as fixed points 17 Celsius Temperature Scale mark as 100 degrees make 100 uniform marks between 0 and 100 degrees Anders Celsius add alcohol food coloring empty glass tube each is 1 degree on the Celsius scale alcohol expands as it warms mark as 0 degrees ice bath boiling water bath 18 6

7 other temperature scales Fahrenheit scale similar to Celsius scale 3 points used 1) ice bath (32 degrees Fahrenheit) 2) ice bath with a compound added (0 degrees Fahrenheit) 3) Daniel Fahrenheit's armpit (96 degrees Fahrenheit) 19 Kelvin Scale based on similar principles to Celsius /Fahrenheit using gases not liquids step sizes same as Celsius scale William Thompson (Lord Kelvin) 0 degrees Kelvin was originally defined as the temperature at which gases would shrink to zero volume 20 converting between temperature scales F = 9/5C + 32 this equation is on your units conversion page converts a temperature from Celsius to Fahrenheit. Example: Convert 37 C to the Fahrenheit temperature. F= 9/5* = = C is about human body temperature 21 7

8 converting Fahrenheit to Celsius rearrange the equation used to convert Celsius to Fahrenheit F = 1.8 C + 32 F - 32 = 1.8 C (F 32)/1.8 = C C = (F-32)/1.8 this equation is on your units conversion page Example: Convert the body temperature of a hibernating hedgehog 26.8 F to degrees Celsius. C = ( )/1.8 = -5.2/1.8 = C hedgehog 22 converting between temperature scales K = C this equation is on your units conversion page converts a temperature from Celsius to Kelvin. Example: Convert 25 C (room temperature) to the Kelvin scale. K= = K = 298 K 23 Intensive vs Extensive Properties Extensive properties of matter depend on the amount of matter considered. Intensive properties do not depend on the amount of matter considered Extensive Intensive cost of a bag candy cost per pound candy? temperature mass density (mass per 1 unit volume 24 8

9 Density intensive property of matter (can be measured on any sample size) D = mass/volume mass is its related extensive property determines if an object will sink or float 25 Measuring Density Density = mass/volume mass and volume must both be measured any sample size OK because density is an intensive property but both mass and volume must be measured on the same sample 26 Measuring Density volume - liquids can be directly measured in glassware - solids with geometric shapes can have their individual length(s) measured and volume calculated irregular shaped solids can be measured by water displacement 27 9

10 Measuring Density what about irregular solids that will dissolve in water, like a chunk of salt? sand could be used instead of a liquid in a liquid displacement-like experiment instead of water a different liquid could be used that the substance would not dissolve in, like oil. 28 Density as a conversion factor conversion factors - new unit. amounts of matter can be described by in units of volume or mass. density = mass/volume volume x density = mass multiply both sides by volume conversion factor new unit 29 Example: Mercury is a metal that is a liquid at room temperature. Mercury metal has a density of 13.6 grams per milliliter (g/ml). What is the mass of 5.0 ml of mercury? 5.0 ml mercury x 13.6 g 1.0 ml = 68 g mercury 30 10

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