Unit Operations and Conversions:

When measuring a value, the units used carry almost as much significance as the actual numerical value itself. For example, stating that the mass of something is 2 says next to nothing about the actual mass of the object. Units are what gives the numerical value physical

significance and how to relate specific objects to others in the universe. It is necessary to

measure things because measurements are key in explaining the physical world around us and in solving mathematical problems.

The most common variables that one measures are length, mass, temperature, and time. Almost everything else that one would measure can be broken down to these 4 things. Below is a table of common units used to express length, mass, time and temperature. Mass is defined as the amount of matter in an object and is typically measured on a scale. Length is defined as a

measured distance or dimension. Time is defined as the period between 2 events and is relative. Temperature is the degree of intensity of the heat in an object.

Base quantity Standard units

Length Foot (ft), meter (m)

Mass Pound (lb), kilogram (kg)

Time Second (s), Minute (min)

Temperature Celsius (°C), Fahrenheit (°F)

Note the different common units for each quantity. These units were given in both the SI and English system of measurement respectively. The SI system of measurement or Système international is the most widely used system of measurement on a global scale. The base units for this system are meters, kilograms, and Celsius. Additionally, there are many other quantities than can be expressed in SI units, most of which will be discussed in detail later. Some additional measurements are volume, area, force, and pressure.

The SI system consists of a system of units of measurement built on base units. These base units are used when the values being measured are much too large or too small to be described using the base value. For example, the size of a small bug wouldn’t be described as 0.003m, instead one would say 3mm. These base units include:

Prefix Value compared

to base unit

Prefix Symbol

Amount needed to make base unit

Mil- 10-3 _{M 1000} Centi- 10-2 C 100 Deci- 10-1 _{D 10} Base 1 1 Deca- 101 da 0.1 Hecto- 102 H 0.01 Kilo- 103 K 0.001 Mega- 106 _{M 0.000001}

The other system of measurement that was included in the prior table was the US Customary Units, or English system of measurement. These include pounds, feet, and Fahrenheit. The English system is used only within the United States and evolved from the previously used imperial or British units.

One of the most basic calculations in Chemical Engineering is unit conversion. It is one of the building blocks for many engineering problems. Now one may ask how to convert from kilograms to grams or centimeters to meters. This can all be done in a simple and systematic way, as each prefix is ten times greater than the previous. Conversion is a multistep process of division and multiplication by a numerical factor, often called a conversion factor. For example, to convert 10 meters to centimeters, it is known that there are 100 cm in 1m. Therefore, the basic procedure to follow is:

10 𝑚 × 100𝑐𝑚

1 𝑚 = 1,000 𝑐𝑚

To convert between units in the SI system, simply create a ratio (using a conversion factor) between the new or desired unit and the current unit. The current units will cancel out, leaving only the value of the new unit.

For the English system of units, conversions between units is a bit more difficult. There are not just a handful of bases or prefixes, but instead a few unique values for different amounts of length and volume. A table of conversions for the English system can be found below. The basic idea of conversions is the same as with SI units: create a ratio of the new unit to the old and multiple this by the old value to generate a new value in desired units.

Length Weight Volume

12 in = 1 ft 16 oz = 1 lb 1 ft3 = 7.48 gal

3 ft = 1 yrd 2000 lb = 1 ton

5280 ft = 1 mi

Units for time are the same in both systems of measurements. The common conversions between time values are:

Time 60 s = 1 min 60 min = 1 hr 24 hr = 1 day 7 days = 1 wk 365 days = 1 year 52 wks = 1 year

It is also possible to convert from SI units to English units and vice versa. This is done in a similar manner by establishing conversion factors or ratios of English to SI units. Below is a table of common unit conversions between systems of measurement.

SI Unit English Unit

2.54 cm 1 in 454 g 1 lb 1 m 3.2808 ft 3.785 l 1 gal 101325 Pa 14.7 psi (lbf/ in2) Temperature:

Temperature is defined as the degree or intensity of heat present in a substance or object. It is the absolute value of molecular motion. The scales for temperature are on a comparative basis. Converting between different temperature units is not as simple as previous conversions. There is not simple ratio to use to convert between the SI and English system of units. Recall that the SI unit of Temperature is Celsius and the English unit is Fahrenheit. In order to convert from

Celsius to Fahrenheit, an equation must be solved. These equations were derived from the basic notion that 212 °F ↔ 100 °C 32 °F ↔ 0 °C At zero, 212-32 = 180 ↔ 100 – 0 180 100= 9 5 To convert from Celsius to Fahrenheit:

F= C*9/5 + 32

To convert from Fahrenheit to Celsius:

C= (F -32)*5/9

Absolute temperature is defined as the thermodynamic zero. It is the temperature of 0 degrees kelvin. Nothing in the universe can get this cold. To convert from Celsius to the SI standard unit of Kelvin of absolute temperature, simply add 273.15 to the temperature in Celsius. To convert from Fahrenheit to Rankine for absolute temperature, simply add 459.7 to the temperature in Fahrenheit.

For the Fahrenheit and Rankine scales, the interval between numbers is equivalent. The same is true for the Celsius and Kelvin scales. For example, a 5 degree Celsius difference is also a 5 degree Kelvin difference. The same does not apply between the Celsius and Fahrenheit scales.

A thermocouple is a device that measures temperature. They function on the creation of a potential difference or voltage drop between 2 different metals. These metals need to have dissimilar properties in order to create the necessary voltage drop. The metal pieces are joined at one end and separated at the other. There is a connection between how a metal conducts heat and electric current. Therefore the heat can develop a voltage drop or current in the metals. This voltage drop can be measured and then converted into a temperature reading. Standards of specific temperature can be used and their voltage drop measured. Then, mathematic equations can be developed in order to relate all future voltage readings to temperature readings.