[Notes] Ch.E Essentials: Units, Measurement, and Problem Solving

E.3 Units of measurement

 

1. SI prefixes 

* 표를 꼭 잘보고 한 두번 더 체크하기.

* 과정 쓸 때 누락하기 말기

1. A note about area (length squared) and volume (length cubed):

When you cube or square the unit, you must do the same to the value. 

1m = 100 cm, 1m^3 = (100cm)^3 = 1,000,000 cm3, 1m^3 = 1X10^6 cm^3 

 

Ex)  A cube has an edge length of 7 cm. If it is divided into 1 cm cubes, how many 1 cm cubes are there? 

volume = l*w*h = 7cm*7cm*7cm = 343 cm^3 ( = 3.43*10^-3)

2. Temperature Scales

 

3. Vocabulary

(1) Accuracy: how close is a measurement to the actual value? 

(2) Precision: how reproducible is the measurement? 

(3) Systematic error: all values are too high or low 

(4) Random error: equal probability high and low 

E.4 Significant figures

1. Counting sig fig

(1) Exact numbers: infinite sig fig Ex) pi, e, counted numbers, conversion factors

(2) Nonzero : always sig fig Ex) 56, 34, …

(3) Zeros:

-- Leading Zeros: not sig EX) 0.00000006 => 1 sig

-- Interior (captive): sig Ex) 306 => 3 sig

--Trailing zeros: sig only if there is a decimal point

* trailing zeros w/o a decimal point are insignificant or ambiguous.

Ex) 30.0 => 3 sf, 30 => ambiguous

 

2. Calculation rules

(1) Multiplication / division: the fewest sig fig

(2) Addition / subtraction: the fewest decimal places

(3) Rounding rules: >=5, round up, <5 keep

 

Ex) (9.18 + 9.2 + 9.157) / 3 = 9.179 => report: 9.2 

3 is the exact number, it will not affect the s.f. 

9.2 is the smallest number of s.g. so report tenth place. 

 

Ex) 2. 5110 x 21.20 / (44.11 + 1.223) 

 

* Always round at the end, x cut digits at every step.

* 계산 할 때 가장 작은 것 (곱셈) 찾기, decimal point (덧셈) 찾기

* exact number 의 sig fig 잘 판단하기

 

E.5 Density

1. Density can be used to identify a substance.

2. Density depends on temperature and does not depend on the amount of substance (intensive property). 

=> unit: g/mL (g/cm^2), g/L

* 단위 환산하는 과정에서 0의 개수 주의 하기

Practice: A small airplane takes on 245 L of fuel. If the density of the fuel is 0.821 g/mL what mass of fuel has the airplane taken on? 

E. 6 Energy

1. Energy: capacity to do work (force through a distance)

2. The total E of an object: the sum of Kinetic E (associated with motion) & Thermal E (associated with object's temperature) & Potential E (associated with object's composition) 

=> systems with high potential E tend to lower their PE to become more stable. 

3. Law of conservation of Energy: In a process, energy is neither created nor destroyed.

(1) Exothermic: system loses E, change in E is negative.

(2) Endothermic: system gains E, change in E is positive.

4. Units of Energy

KE = 1/2mv^2 | Units: (kgm^2)/s^2 

1(kgm^2)/s^2 = 1 Joule

1 cal = 4.184J

1000 cal = 1 kcal = 1 Cal (nutritional) 

E.7,8,9  Problem Solving

1. 계산 과정 명확하게 쓰기.

2. 계산기 실수하지 말고 계산 시 한 번씩 더 확인

3. 문제 제대로 읽고 파악한 후 계산  

 

Ex) Convert 1.37 ounces of silver to milligrams of silver, given 1 oz = 28.35 g 

 

Practice: A house has an area of 1,235 ft^2. What is the area in km^2? 

Practice: A cylinder has a length of 10.0 cm, a radius of 1.0 cm, and a mass of 3.0 g. What is the density of the cylindrical substance in g/cm3? V_cylinder = 𝜋𝜋r^2h 

Practice: Polluted air can have carbon monoxide (CO) levels of 15.0 ppm. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many milligrams of carbon monoxide does the average person inhale in an 8-hour period in this level of carbon monoxide pollution? Assume that the CO has a density of 1.2 g/L. (Hint: 15.0 ppm CO means 15.0 L CO per 106 L air.)