Temperature Scales
Temperature is a physical parameter that indicates how hot or cold something is. It is required especially for the calculation of the average kinetic energy of the particles in an item. This is a form of energy that is related to movement. But how can someone tell how hot it is and how chilly it is? The phrases “hot” and “cold” are not scientific in nature. When describing how hot or cold something is, we must mention temperature. Using temperature instead of the phrases hot or cold can help to clear up any misunderstandings. Let’s understand the temperature and different scales to measure it in this article.
What is Temperature?
The hotness or coolness of a body is referred to as its temperature. It is a method of estimating the kinetic energy of particles within a body.
The faster the particles travel, the higher the temperature, and vice versa. Temperature is vital in many branches of science, from physics to geology, and it is also significant in many parts of our daily lives.
Temperature is measured using thermometers using well-defined scales. Fahrenheit, Celsius, and Kelvin are the three most prevalent temperature scales. Identifying two consistent temperatures yields temperature scales. Water freezing and boiling temperatures at ordinary atmospheric pressure are often applied.
Thermometer
The thermometer based on the expansion of a liquid the mercury-in-glass thermometer was invented in the seventeenth century. At that time completely arbitrary scales were used so that readings of any two thermometers had wide disparity. This problem was, however, removed when common scales of temperature were devised in the first half of the eighteenth century.
A thermometer can be based on any physical attribute that is consistently and reproducibly affected by temperature. For most substances, for example, volume increases with temperature. This feature serves as the foundation for the ordinary alcohol thermometer as well as the early mercury thermometers.
In defining the common temperature scales, two conveniently reproducible temperatures, called fixed points, are used:
- The upper fixed point is the temperature of steam from water boiling under an external pressure of 76 cm of Hg at sea level and 45° latitude (under normal atmospheric pressure).
- The lower fixed point is the temperature of pure melting ice under an external pressure of 76 cm of Hg at sea level and 45° latitude (under normal atmospheric pressure).
- The Centigrade scale was first introduced by Anders Celsius. So it is also called the Celsius scale, in which the lower fixed point is chosen as 0 °C and the upper fixed point is chosen as 100 °C. This scale is in common use in most countries.
- There is another important scale of temperature. It is called the Fahrenheit scale and was introduced by Gabriel Daniel Fahrenheit. On this scale, the lower fixed point is chosen as 32 °F and the upper fixed point is chosen as 212 °F.
- The interval between the fixed point marks in a thermometer is called the fundamental interval. It is divided into 100 equal spaces for Celsius scale Fahrenheit divided into 100 equal spaces for the Celsius scale, or 180 for the Fahrenheit scale, to give the individual degrees. Above and below the fixed points, the scale may be extended by marking off degrees of the same size.
Temperature Scales
Temperature is measured using thermometers using well-defined scales. There are several techniques for converting temperatures. Water has a freezing point of 273.15 K and a boiling point of 373.15 K on the Kelvin scale. Water has a freezing point of 32 °F and a boiling temperature of 212 °F on the Fahrenheit scale.
There are mainly three temperature scales commonly used:
- Celsius Scale: The Celsius temperature scale, commonly known as the centigrade temperature scale, is based on zero for the freezing point of water and one hundred for the boiling point of water. It was invented in 1742 by the Swedish astronomer Anders Celsius and is commonly referred to as the centigrade scale due to the 100-degree range between the setpoints.
- Fahrenheit Scale: The melting point of ice is 32 degrees Fahrenheit on the Fahrenheit temperature scale. Water has a boiling point of 212 degrees Fahrenheit, and the gap between the two is split into 180 equal parts. Each division equals one degree. The absolute zero temperature in Fahrenheit is 459.7 degrees Fahrenheit.
- Kelvin Scale: In the International System of Measurement (SI), the Kelvin temperature scale is the foundation unit of thermodynamic temperature measurement. It is defined as 1/ 273.16 of pure water’s triple point (equilibrium between the solid, liquid, and gaseous phases). An absolute temperature scale named after William Thomson, Baron Kelvin, a British scientist.
The following table represents the lower and upper fixed points along with their fundamental interval and symbols for each type of temperature scale:
| Scale | Lower fixed point | Upper fixed point | Fundamental interval | Symbol |
1. | Celsius | 0 | 100 | 100 | K |
2. | Kelvin | 273 | 373 | 100 | °C |
3. | Fahrenheit | 32 | 212 | 180 | °F |
Correspondingly, three major temperature conversions or relation between each scale, such as Conversion between:
- Kelvin to Celsius
Both the Kelvin and the Celsius scale have a fundamental interval is 100 degrees.
Therefore,
100 divisions on the Kelvin scale = 100 divisions on the Celsius scale
1 division on the Kelvin scale = 1 division on the Celsius scale
This implies,
1°C = 1 K
Now the lower fixed point in the Kelvin scale is 273 °C so if an unknown temperature reads T_{K} in Kelvin scale, then for this reading the mercury thread has moved (T_{K} – 273 °C) divisions from the lower fixed point. In the Celsius scale, the lower fixed point is 0 °C so if the same temperature reads t_{°C} in this scale, then this reading corresponds to a movement of t divisions of the mercury thread from the lower fixed point. As 1 division on both the scales are equal, so
T_{K} – 273 °C = t_{°C}
T_{K} = 273 °C + t_{°C}
Hence, the temperature reading in the Kelvin scale may be obtained by adding 273 to that in the Celsius scale.
- Celsius to Fahrenheit or Fahrenheit to Celsius
The fundamental interval in the Celsius scale is 100 divisions and that in the Fahrenheit scale is 180 divisions.
Therefore,
180 divisions on the Fahrenheit scale = 100 divisions on the Celsius scale
1 division on the Fahrenheit scale = (5/9) divisions on the Celsius scale.
1 division on the Celsius scale = (9/5) divisions on the Fahrenheit scale.
Thus, 1 °C = (9/5) °F or. 1 °F = (5/9)° C
Let us suppose that an unknown temperature reads C and F on the Celsius and the Fahrenheit scales respectively. Now, the reading F corresponds to the movement of (F-32) divisions of the mercury thread from the lower fixed point which is 32° C. Similarly, the reading C corresponds to a movement of C divisions from the lower fixed point which in this case is 0° C.
(F-32) divisions on the Fahrenheit scale=C divisions on the Celsius scale. ……(1)
1 division on the Fahrenheit scale = (5/9) divisions on the Celsius scale.
(F-32) divisions on the Fahrenheit scale = (5/9)(F-32) divisions on the Celsius scale. ……(2)
From equations (1) and (2),
C = (5/9) × (F-32)
(C/5) = [(F-32) / 9]
- Kelvin, Celsius, and Fahrenheit
If an unknown temperature reads K, C, and F on the Kelvin, Celsius and Fahrenheit scales respectively,
Since, it is known that:
C = K – 273 and (C / 5) = [(F – 32) / 9]
Therefore,
C / 5 = (F – 32) / 9 = (K – 273) / 5
Sample Problems
Problem 1: Mercury freezes at -39 °C and boils at 357 °C in the atmosphere: pressure. Convert it to Fahrenheit temperatures.
Solution:
We have, (C/5)=[(F-32)/9]
At C_{1}=-39°C
Or (-39/5)=(F-32)/9
Or -351=(5F-160)
So, F=-38.5°
At C_{2}=357°C
Or (357/5)=(F-32)/9
Or 3213=(5F-160)
So, F = 674.6° F
Problem 2: The temperature of dry ice at normal pressure -109 °F. Is this hotter or colder than the temperature of boiling ethane which at -88 °C?
Solution:
At F=-109°F
We have, (C/5)=[(F-32)/9]
Or (C/5)=[(-109-32)/9]
C=-78.3°C
The temperature of Dry ice is greater than boiling ethane.
So, dry ice is hotter.
Problem 3: At what temperature will the Centigrade thermometer read twice as much as the Fahrenheit thermometer?
Solution:
Let x be the temperature on the Fahrenheit thermometer and 2x on the Centigrade thermometer
We have, (C/5) = [(F-32)/9]
(2x/5) = [(x-32) / 9]
18x = 5x -160
13x = -160
x = -12.3
The required temperature is -12.3°F or -24.6°C.
Problem 4: Two thermometers-one reading in Celsius and the other in Fahrenheit were successively dipped into two baths. In both cases, the difference in the readings between the two thermometers was found to be 20. If the baths were at different temperatures, find their temperatures on the Celsius scale.
Solution:
Let the temperatures of the baths in the Celsius scale be X°C and Y°C. On the Fahrenheit scale, the temperature of the first bath is (X+20)°F and that of the second bath evidently (Y-20)°F.
We have, (C/5) = [(F-32) / 9]
First Bath,
(X/5) = (X+20-32) / 9
9X = 5X-60
X = -15°C.
Second Bath,
(Y/5) = (Y-20-32) / 9
9Y = 5Y-260
Y= -65°C.
Problem 5: What are the lower and upper fixed points of a thermometer?
Solution:
Upper fixed point: The upper fixed point is the temperature of steam from water boiling under an external pressure of 76 cm of Hg at sea level and 45° latitude (under normal atmospheric pressure).
Lower fixed point: The lower fixed point is the temperature of pure melting ice under an external pressure of 76 cm of Hg at sea level and 45° latitude (under normal atmospheric pressure).
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