Section 1_Mathematical Basics_Class(1).pptx

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1. ENGINEERING PHYSICS CHEM IA (PHYSCA1) 2022 You are welcome to the Engineering Physics Chem IA (PHYSCA1 ) Module for B. Eng. Tech. (Chemical Engineering) 2023/02/22 1

2. Section 1: Mathematical Basics Units of measurement Scientific Notation Prefixes of Ten Trigonometry Logarithms Unit Conversion Dimensional Analysis Significant Figures 2023/02/22 2

3. What is the name of this building? 2023/02/22 3

4. The Burj Khalifa 2023/02/22 4 Located in Dubai, UAE 830 m tall (to the tip) 163 floors Took almost 5 yrs to construct Tallest building in the world

5. SPOT TEST Question 1 Define the term “Physics”. Question 2 Why do you think Physics is relevant to your intended programme of study (Chemical Engineering) ? Give FIVE reasons. 2023/02/22 5

6. Definition of Physics The word Physics originates from the Greek word “ phusis ” (modern Greek), which means NATURE . In ancient Greek: “ phusike ”, which means “KNOWLEDGE OF NATURE ”. In Latin: “ physica ”, which means “ NATURAL SCIENCE”. 2023/02/22 6

7. PHYSICS is the study of the laws and principles that govern the behaviour of nature or the natural world in which we live. Physics encompasses a remarkable variety of phenomena such as: planetary orbits radio and TV waves fluid dynamics/statics colour and many more! Definition of Physics 2023/02/22 7

8. Units of measurement Physics is an empirical science . It involves observation , analysis and experiment . Physics experiments involve the measurement of a variety of physical quantities. These measurements must be accurate and reproducible . The first step in ensuring accuracy and reproducibility is defining the units in which the measurements are made. 2023/02/22 8

9. Units of measurement How is reproducibility ensured? The General Conference on Weights & Measures. 2023/02/22 9

10. There are THREE systems of units used worldwide, namely The SI system ( Systeme ’ Internationale ) The c.g.s . system The British Engineering (BE) system Units of measurement 2023/02/22 10

11. Units of measurement There are TWO types of units, namely: Base Units Derived Units 2023/02/22 11

12. 1) The S.I. system employs the following base units: metre (m): length/distance kilogram (kg): mass second (s): time ampere (A): electric current kelvin (K): temperature candela (cd): luminous intensity mole ( mol ): amount of substance Units of measurement 2023/02/22 12

13. NOTE : Units named after people are abbreviated using capital letters otherwise lower cases are used. Base units are used in combination to define additional units for other important physical quantities. Such units are referred to as DERIVED units. Units of measurement 2023/02/22 13

14. Name as many derived units as you can and also provide their respective physical quantities. Units of measurement: Class Exercise 2023/02/22 14

15. 2) The c.g.s . system employs the following : c entimetre, g ram and s econd. 3) The BE system employs the following: Force/Weight : pound ( lb ). Mass : slug ( sl ), ounce ( oz ). Length : inch (in), mile (mi), foot ( ft ). Temperature : degrees Fahrenheit ( o F ). Units of measurement 2023/02/22 15

16. State whether the following units are S.I. or B.E. Mention the physical quantity each one measures. ton h) Btu yard i) horsepower furlong j) calorie pint k) atomic mass unit quart l) torr gallon m) watt acre n) electron volt Units of measurement: HOMEWORK 2023/02/22 16

17. SECTION 1: Introduction to Basics Units of measurement √ Scientific Notation Prefixes of Ten Trigonometry Logarithms Unit Conversion Dimensional Analysis Significant Figures 2023/02/22 17

18. Scientific notation is a method that is used to help write very large and very small numbers in a shorter form by using the powers of ten. In this notation, the decimal point in a number is displaced either to the left or right a certain number of times until there is only ONE digit before the decimal. Scientific Notation 2023/02/22 18

19. Scientific Notation: Example 1 2023/02/22 19 Write the following numbers in a scientific notation (correct to 2 decimal places): 2000 m 8600000 Hz 362850 kg 0.0000035 m 0.0012 s

20. SECTION 1: Introduction to Basics Units of measurement √ Scientific Notation √ Prefixes of Ten Trigonometry Logarithms Unit Conversion Dimensional Analysis Significant Figures 2023/02/22 20

21. Prefixes of Ten 2023/02/22 21

22. Prefixes of Ten: Example 2 2023/02/22 22 Rewrite the answers in Example 1 using prefixes of 10 2000 m 8600000 Hz 362850 kg 0.0000035 m 0.0012 s

23. SECTION 1: Introduction to Basics Units of measurement √ Scientific Notation √ Prefixes of Ten √ Trigonometry Logarithms Unit Conversion Dimensional Analysis Significant Figures 2023/02/22 23

24.   Unit Conversion 2023/02/22 24

25. 1. In all calculations, write down the units explicitly. Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically. Be guided by the fact that multiplying or dividing an equation by a factor of 1, does not alter the equation. Unit Conversion: Reasoning Strategy 2023/02/22 25

26. The tallest building in the world is the Burj Khalifa in Dubai, with a height of 830m. Express this height in feet ( ft ) kilometres (km) centimetres (cm) millimetres (mm) 2023/02/22 26 Unit Conversion: Example 3

27. GENERAL KNOWLEDGE 2023/02/22 27 1) Which building is the tallest in Africa and in which country is it located?

28. 2023/02/22 28

29. GENERAL KNOWLEDGE 2023/02/22 29 2) Which building is the tallest residential building in Africa and in which country is it located?

30. 2023/02/22 30

31. GENERAL KNOWLEDGE 2023/02/22 31 3) What is the meaning of the symbol “℮”, written after the expression of a unit of volume or mass? e.g. 125 ml ℮ or 250 g ℮

32. 2023/02/22 32

33. Do problems 1, 2, 4, 5, and 6 in Chapter 1 on pages 18-19 ( Cutnell 10 th Edition) Estimate your age in seconds (Use fact that a year has 365 days & do your calculation to the day) Self Assessment 2023/02/22 33

34. SECTION 1: Introduction to Basics Units of measurement √ Scientific Notation √ Prefixes of Ten √ Unit Conversion √ Dimensional Analysis Significant Figures 2023/02/22 34

35. x = displacement [m], v = velocity [ m . t = time [s] NOTE : The constant , must not be considered in dimensional analysis.   Is the following equation dimensionally correct? Dimensional Analysis: Example 4 2023/02/22 35

36. Is the following equation dimensionally correct? Dimensional Analysis: Example 5 2023/02/22 36

37. Do problems 3 and 7 in Chapter 1 on page 19 Self Assessment: Cutnell (10 th Edition) 2023/02/22 37

38. SECTION 1: Introduction to Basics Units of measurement √ Scientific Notation √ Prefixes of Ten √ Unit Conversion √ Dimensional Analysis √ Significant Figures 2023/02/22 38

39. Example: Unit Conversion 2023/02/22 39 Convert 1000 μ g.mm.n to kg.m .  

40. Significant Figures Suppose we want to verify the value of π . First we need to define π . “pi” is defined as the ratio of the circumference of a circle to its diametre . Given : Circumference = 424 mm Diametre = 135 mm Thus, π = 3.140740741 ( NOTE: no units! ) 2023/02/22 40

41. Significant Figures In terms of the correct number of significant figures, how would you express the final answer? Answer : 3.14 2023/02/22 41

42. Significant Figures The number of significant figures in a result is simply the number of figures that are known with some degree of reliability or precision. Alternatively, The significant figures of a number are those digits that carry meaning and are contributing to its precision. 2023/02/22 42

43. Significant Figures: Rules RULE 1 : All non-zero digits are significant . e.g. 34.7 has THREE significant figures. RULE 2 : Zeros appearing anywhere between two non- zero significant digits are significant . e.g. 5021 has FOUR significant figures. RULE 3 : Leading zeros are not significant . e.g. 0.00053 has TWO significant figures. 2023/02/22 43

44. RULE 4 : Trailing zeros in a number containing a decimal point (i.e. to the right of the decimal point) are significant . e.g. 45.00 has FOUR significant figures. 0.00034500 has FIVE significant figures. RULE 5 : Trailing zeros in a whole number with no decimal shown are not significant . e.g. 320 has TWO significant figures. Significant Figures: Rules 2023/02/22 44

45. RULE 6 : For a number in scientific notation: N 10 x , all digits comprising N are significant by the first 5 rules: “10” and “x” are not significant. e.g. 5.02 10 3 has THREE significant figures   Significant Figures: Rules 2023/02/22 45

46. Significant Figures: Example 6 State the number of significant figures in each of the following numbers & mention the Rule(s) used thereof: a) 424 mm 3 s.f. : Rule 1 b) 135 mm 3 s.f. : Rule 1 c) 61 g 2 s.f. : Rule 1 2023/02/22 46

47. Significant Figures: Example 6 (cont.) State the number of significant figures in each of the following numbers & mention the Rule(s) used thereof: d) 1.234 g 4 s.f. : Rule 1 e) 48.923 kg 5 s.f. : Rule 1 f) 5004 mm 4 s.f. : Rules 1 & 2 2023/02/22 47

48. Significant Figures: Example 6 (cont.) State the number of significant figures in each of the following numbers & mention the Rule(s) used thereof: g) 3.07 s 3 s.f. : Rules 1 & 2 h) 0.20 g 2 s.f. : Rules 1, 3 & 4 i) 8.1000 m 5 s.f. : Rules 1 & 4 2023/02/22 48

49. Significant Figures: Example 6 (cont.) State the number of significant figures in each of the following numbers & mention the Rule(s) used thereof: j) 501.040 J 6 s.f. : Rules 1, 2 & 4. k) 0.0004 s 1 s.f. : Rules 1 & 3 . l) 10.0 g 3 s.f. : Rules 1 & 4 . 2023/02/22 49

50. Significant Figures: Example 6 (cont.) State the number of significant figures in each of the following numbers & mention the Rule(s) used thereof: m) 3 s.f. : Rules 1, 2 & 6. n) 5 s.f. : Rules 1, 2, 4 & 6. o) 3 s.f. : Rules 1, 4 & 6.   2023/02/22 50

51. Significant Figures: Example 6 (cont.) State the number of significant figures in each of the following numbers & mention the Rule(s) used thereof: p) 190 s 2 s.f. : Rules 1 & 5 q) 1020 L 3 s.f. : Rules 1, 2 & 5 r) 50600 m 3 s.f. : Rules 1, 2 & 5 2023/02/22 51

52. Significant Figures: Multiplication/Division When multiplying or dividing, the number of significant figures in the final calculated value will be the same as that of the quantity with the fewest number of significant figures used in the calculation. 2023/02/22 52

53. Significant Figures: Addition/Subtraction When adding or subtracting the calculated value will have the same number of digits to the right of the decimal point as that of the least precise quantity. 2023/02/22 53

54. Significant Figures: Example 7 Express your answer to the correct number of significant figures: 1) 37.76 + 3.907 + 226.4 = ? Ans.: 268.1 2) 319.15 – 32.614 = ? Ans.: 286.54 2023/02/22 54

55. Significant Figures: Example 7 (cont.) 3) 125 – 0.23 + 4.109 = ? Ans.: 129 4) 2.02 2.5 = ? Ans.: 5.1 5) 600.0 5.2302 = ? Ans.: 114.7  

56. Significant Figures: Example 7 (cont.) 6) 0.556 Ans.: 4 7) 45 3.00 = ? Ans.: 1.4 8) (27.2 15.63) 1.846 = ? Ans.: 2.30 or 230.  

57. 9) 104.630 + 27.08362 + 0.61 = ? Ans.: 132.32 10) 0.0032 273 = ? Ans.: 0.87 11) Ans.: 1.7   Significant Figures: Example 7 (cont.) 2023/02/22 57

58. 12) 3.00 1.5 = ? 13) [(10.3) + (0.01345)] [(10.3) 0.01345)] = ?   Significant Figures: HOMEWORK 2023/02/22 58

59. SUMMARY Units are supposed to be specified in all final answers. You may not show units during the substitution steps. Very large numbers & very small numbers MUST be expressed in a scientific notation. Significant figures MUST be observed at all times in all calculations. Marks will be deducted if items 1-3 are not adhered to. 2023/02/22 59

60. SECTION 1: Introduction to Basics Units of measurement √ Scientific Notation √ Prefixes of Ten √ Unit Conversion √ Dimensional Analysis √ Significant Figures √ 2023/02/22 60