LECTURE NOTE 3 The metric system offers simplicity and basic unit. Although the English system was common, a committee was for over ten and a new system was agreed on called Metric system. Physical Quantity Length Mass Volume Time Basic Metric unit Meter Gram Liter Second Symbol m g L S METRIC PREFIXES Metric system is a decimal system but uses a prefix to express a multiple or a fraction of a basic unit. A metric prefix increases or decreases a basic unit by a factor of 10. PREFIX SYMBOL MULTIPLE/FRACTION giga G 1,000,000,000=1x10 9 mega M 1,000,000= 1x10 6 kilo K 1,000 = 1x 103 deci d 0.1=1x10 -1 centi c 0.01=1x10 -2 milli m 0.001=1x10-3 Micro µ 0.000001=1x10-6 nano n 0.000000001=1x10-9 The metric system is sometimes referred to as International system of measurement (SI), but SI is an extension of metric system. The SI system is more comprehensive and sophisticated. The international system of units has the following as base units. Physical Quantity SI basic unit Symbol length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Electric current Ampere A Light intensity Candela cd Amount of substance mole mol METRIC-ENGLISH CONVERSIONS Most part of the world, the metric system is used, however, some parts of America still uses the English system. The following can be used as Metric-English conversion table: Physical Quantity English Unit Metric Unit Length 1 inch(in) 1in=2.54cm Mass 1 pound(lb) 1lb=454g 1 Volume Time 1 quart(qt) 1 second(sec) 1qt=946mL 1sec=1.00s VOLUME BY CALCULATION The volume of a rectangular solid is equal to length multiplied by width multiplied by thickness. Volumes of a regular solid can be calculated. Students must however take note of the unit of the parameters given and the unit of the answer, they must all be in the same units. Example: A sheet of tin measures 35.0cm by 25.0cm, and the volume is 1.36cm3. What is the thickness of the foil in centimeters? V=L x W x thickness Thickness= V WxL =1.36cm3 25.0cm x 35.0cm =0.00155cm =1.55x10-3cm CUBIC VOLUME AND LIQUID VOLUME In metric system, the basic unit of liquid volume is liter. A Liter is equivalent to the volume occupied by a cube exactly 10cm on a side. A cube is a solid, V= length x Width x thickness V= 10cm x 10cm x10cm V= 1000cm3 Recall 1L= 1000mL, combining, 1000cm3 = 1L = 1000mL Therefore, 1cm3 = 1 mL VOLUME BY DISPLACEMENT Volume of liquids can be measured with calibrated glassware. Volume of regular solid on the other hand can be measured by calculations; the volumes of irregular solids cannot be measured using volume measured or by calculations Volume of irregular solids or gases can be measured indirectly by the amount of water it displaces. The volume of water is taken before emersion of the solid or in the case of gases, before the experiment is started. V (final) – V (initial) = V (displaced) DENSITY The term density expresses the concentration of mass. Density is the amount of mass per volume. Density (d) = mass (g) Volume (cm3) The units for solids and liquids: g/cm3 or g/mL. The unit of gases: g/L 2 Density varies slightly with temperature (but we will ignore this small effect for now). Density of gases however, varies greatly with temperature and pressure. Metric standard for mass and volume were based on water; a mass of 1kg was set equal to 1L volume of water. Therefore density of water is 1kg/L which is equal to 1g/ml or 1.00g/mL When you have three liquids with different densities in the same container, you will observe three layers of liquids. The one with the highest density stays in the bottom of the container, while the one with the next lower density floats on top of the one at the bottom, the one with the least density floats on top of the second one. APPLYING DENSITY AS A UNIT FACTOR Since density relates mass and volume, it can be used as a unit factor. For example, the density of mercury is 13.6g/mL, The unit equation will be: 13.6g = 1mL The unit factor will be: 13.6g = 1mL 1ml 13.6g Example A 1.00-in cube of copper measures 2.54cm on a side. What is the mass of copper cube? (Given: d of copper = 8.96g/cm3) 8.96g = 1cm3 --------- unit equation 1cm3 = 8.96g 8.96g 1cm3 Finding the volume of the cube: V = L x W x T =2.54cm x 2.54cm x2.54cm =16.4cm3 16.4cm3 x 8.96g 1cm3 =147g SPECIFIC GRAVITY This is the ratio of the density of a liquid to the density of water at 40C Specific gravity (sp gr) is unit less because the density units cancel out. The density of water is 1.00g/cm3 while specific gravity of water is 1.00. TEMPERATURE Hotness or coldness of the atmosphere is determined by how fast the tiny air molecules are moving. If the temperature is warmer, molecules move faster and have more energy while they move slower with less energy when cooler. Temperature is a measure of the average kinetic energy of an individual particle. The instrument used to measure temperature is thermometer. Gabriel Fahrenheit, a German scientist invented the mercury thermometer. He got two ranges of readings from a bath of ice, which he gave 0, and the temperature from his underarm, which he gave 96. And so he calibrated the thermometer from 0 to 96, each division is called Fahrenheit degree (0F). The scale was elevated to freezing and boiling point of water as the standard reference point. The freezing point of water was assigned 320F while the boiling was 3 assigned 2120F. The Fahrenheit scale later became the basic unit for English system of measurement. Anders Celsius, proposed a similar scale, but on his scale, the freezing point of water was assigned 00C while the boiling point was assigned 1000C. The scale was divided into 100 parts, each division called 10C.The Celsius degree is also referred to as a centigrade degree and is a basic unit in the metric system. William Thomson (Lord Kelvin), proposed a scale based the lowest possible temperature. The unit temperature was Kelvin unit (K), a basic unit in the S.I. unit. On Kelvin scale, the coldest temperature is assigned 0K, each division is equal to 10C. The lowest temperature is called ABSOLUTE ZERO = -273.150C 0K is equivalent to -2730C Freezing point of water is 273K Boiling point of water is 373K Converting from one Scale to Another 00C = (0F – 320F) 1000C 1800F 0 F = (C x 1800F) +320F 1000C 0oC + 273 = K HEAT AND SPECIFIC HEAT Heat is the flow of energy from object at higher temperature to an object at lower temperature. Heat and temperature are both a measure of kinetic energy. Heat measures total energy while temperature measures average energy. Heat is expressed in unit of calories or kilocalories. A calorie (cal) is the amount of heat necessary to raise 1g of water 1degree on the Celsius scale. A kilocalorie (kcal) is the amount of heat necessary to raise 1000g of water 1 degree on the Celsius scale. A food calorie (Cal) is spelled with a capital letter to distinguish it from metric calorie. 1 Cal (food calorie) = 1 kcal (1000 cal) The S.I. unit for energy is Joule (J) 1 cal = 4.184 J The heat produced by chemical reactions is often expressed in kilocalorie, and kilojoules (kJ). 1kcal = 4.184kJ SPECIFIC HEAT Specific heat is the heat required to bring about a given change in temperature. The surface of the earth is covered with water, and fortunately its high specific heat helps to regulate climate and maintain moderate temperature. Specific heat (sp ) is the heat required to raise the temperature of 1g of a substance by 1oC. The unit of specific heat is calories per gram per 0C. Specific heat (cal/g0C) = heat (cal) Mass (g) x temperature change (0C) 4