Temperature And Its Scales

Temperature is a fundamental concept in science that measures how hot or cold an object is. It's an essential part of everyday life, influencing everything from the clothes we wear to how we cook food. For instance, we check the temperature to decide if we need a jacket or to ensure the oven is set right for baking a cake. Temperature also plays a crucial role in technology and health, from monitoring weather forecasts to measuring body temperature during illness. There are different scales to measure temperature, such as Celsius, Fahrenheit, and Kelvin, each suited to specific fields. For example, while Celsius is common in daily life, scientists often use Kelvin for precise calculations. Understanding temperature scales helps us navigate both everyday tasks and scientific explorations.

Temperature And Its Scales

Temperature is a measure of the degree of heat present in an object or environment, affecting the behaviour of substances in everyday life and in scientific contexts. It helps us determine whether something is hot or cold, guiding our decisions from adjusting air conditioners to setting oven temperatures while cooking. Temperature is also critical in various industries, such as refrigeration, metallurgy, and healthcare, where precise control is essential. To quantify temperature, different scales are used globally, including Celsius, Fahrenheit, and Kelvin. Each scale serves distinct purposes: Celsius is commonly used in most countries for daily temperature measurement, Fahrenheit is mainly used in the United States, and Kelvin is the standard in scientific research, particularly in understanding absolute temperatures.

Let's discuss one by one

Temperature

Temperature is the degree of hotness or coldness of a body. Heat always flows from high temperature to low temperature if no external work is applied.

Temperature is one of the seven fundamental quantities and its dimension is $[\theta]$. S.I. unit of temperature is Kelvin.

Scales of Temperature

To construct any scale of temperature, we have to take two fixed points. The first fixed point is the freezing point (ice point) of water. The second fixed point is the boiling point (steam point) of water.

Celsius scale: In this scale, the ice point is taken at 0° and the steam point is taken at 100°. The temperature measured on this scale is all in degrees Celsius(°C).

Fahrenheit scale: This scale of temperature has a freezing point of 32°F and a steam point of 212°F.

Kelvin scale: The Kelvin temperature scale is also known as the thermodynamic scale. The temperature measured on this scale is in Kelvin (K).

Note - The triple point of water is also selected to be the zero of the scale of temperature

The temperature on any scale can be converted into any other scale by using the following formula

$\frac{(\text { Reading on any scale }- \text { Ice point })}{(\text { Steam point }- \text { ice point })}$

All the above-mentioned temperature scales are related to each other by the following relationship

$\frac{C}{5}=\frac{F-32}{9}=\frac{K-273}{5}$

The table below shows the range of various temperature scales

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Solved Examples Based On Temperature And Its Scales

Example 1: The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between the upper fixed point and the lower fixed point, there are 150 equal divisions of scale $P$ and 100 divisions on scale $Q$. The relationship for conversion between the two scales is given by:-

1) $\frac{t_p}{100}=\frac{t_Q-180}{150}$
2) $\frac{t_Q}{150}=\frac{t_P-180}{100}$
3) $\frac{t_p}{180}-\frac{t_Q-40}{100}$
4) $\frac{t_Q}{100}=\frac{t_P-30}{150}$

Solution

$\begin{aligned} & \frac{t_p-30}{180-30}=\frac{t_Q-0}{100-0} \\ & \frac{t_p-30}{150}=\frac{t_Q}{100} \\ & \frac{t_Q}{100}=\frac{t_p-30}{150}\end{aligned}$

Hence, the answer is the option (4).

Example 2: On a temperature scale ' X ', the boiling point of water is $65^0 \mathrm{X}$ and the freezing point is $-15^0 \mathrm{X}$. Assume that the X scale is linear. The equivalent temperature corresponding to the Fahrenheit scale would be :

1) $-63^0 \mathrm{~F}$
2) $-148^0 \mathrm{~F}$
3) $-48^0 \mathrm{~F}$
4) $-112^0 \mathrm{~F}$

Solution:

$\begin{aligned} & \frac{X_T-X_L}{X_H-X_L}=\frac{T_F-32}{212-32} \\ & \frac{-95^{\circ}-\left(-15^{\circ}\right)}{65^{\circ}-\left(-15^{\circ}\right)}=\frac{T_F-32}{180} \\ & \frac{-80^{\circ}}{80^{\circ}}=\frac{T_F-32}{180^{\circ}} \\ & -180=T_F-32 \\ & T_F=-180+32=-148^{\circ} \mathrm{F}\end{aligned}$

Hence, the answer is the option (2).

Example 3: On linear temperature scale Y, water freezes at 160^o Y and boils at - 50^o Y. On this Y scale, a temperature of 340 K would be read as : ( water freezes at 273 K and boils at 373 K )

1) $-73.7^{\circ} Y$
2) $-233.7^{\circ} \mathrm{Y}$
3) $-86.3^{\circ} \mathrm{Y}$
4) $-106.3^{\circ} Y$

Solution:

Since the temperature scale is assumed to be linear, the slope in the two cases will be the same. Hence,
$\begin{aligned} & \frac{Y-(-160)}{-50-(-160)}=\frac{K-273}{373-273} \\ & \frac{Y+160}{110}=\frac{K-273}{100} \\ & Y=\frac{11}{10}(K-273)-160 \\ & Y=\frac{11}{10}(340-273)-160=-86.3^0 Y\end{aligned}$

Hence, the answer is the option (3).

Example 4: The graph PQ shown in the figure is a plot of the temperature of a body in degrees Celsius and degrees Fahrenheit. Then, the slope of line PQ is

1) $\frac{3}{5}$
2) $\frac{5}{3}$
3) $\frac{9}{5}$
4) $\frac{5}{9}$

Solution:

Slope of PQ

$\begin{aligned} & =\frac{y_2-y_1}{x_2-x_1} \\ & =\frac{100-0}{212-32} \\ & =\frac{100}{180}=\frac{5}{9}\end{aligned}$

Hence, the answer is the option (4).

Example 5: What is the value of $-196^{\circ} \mathrm{C}$ in the Kelvin scale

1) 87

2) 77

3) 107

4) 117

Solution:

Kelvin Scale

The Kelvin temperature scale is also known as the thermodynamic scale.

wherein

The temperature measured on this scale is in Kelvin(K).

$\begin{aligned} & T_k=273+T_C \\ & =273+(-196 C) \\ & T_k=77 \text { Kelvin }\end{aligned}$

Hence, the answer is the option (2).

Summary

Temperature is a measure of the average kinetic energy of the particles in a substance; it indicates if a substance is hot or not. It has several temperature scales though, the most commonly used being Celsius, Fahrenheit, and Kelvin. Celsius is the one mainly used by the majority worldwide and is defined as it states that 0°C represents the freezing point and 100°C the boiling point. Fahrenheit is used mainly in the USA, and it defines the freezing point of water at 32°F and the boiling point at 212°F. Kelvin is used mainly for scientific purposes, whose zero point thermodynamically corresponds to absolute zero—the point at which the particles are in minimum thermal motion—but has a gradation like Celsius, so the freezing point of water is 273.15 K and the boiling point is 373.15 K. These scales allow us to do much, from the simplest use in weather forecasting to high-end scientific research applications to purposes in our lives.