Heat and Temperature

This note covers Heat, Temperature, and Temperature Scales — part of the SSC Physics chapter Effect of Heat on Matter. Explore related notes on Thermal Expansion, and Specific Heat, Latent Heat from the same chapter below.

1. Fundamentals of Heat and Temperature

Heat

Until the latter part of the 18^th century, scientists believed that heat was a type of extremely subtle fluid or gaseous substance called caloric. Hot objects contained more caloric, while cold objects contained less. If caloric entered an object, it became hot, and if it left, it became cold.

In 1798, Count Rumford proved that caloric does not actually exist, and that heat is closely related to motion. While drilling holes into pieces of metal to make cannon barrels, he noticed that the tiny metal chips flying off were extremely hot. He reasoned that the heat originated from the mechanical work expended in operating the drill. This mechanical work imparts kinetic energy to the molecules of the metal pieces, heating them up.

In fact, heat is the result of the random motion of a substance's molecules. The molecules of a substance are always in motion. The total amount of heat in any substance is proportional to the total kinetic energy of its constituent molecules. If heat is supplied to an object, the random motion of its molecules increases, consequently increasing its kinetic energy. Heat is a form of energy associated with the molecular motion of matter that produces the sensation of hot or cold. Heat is a form of energy because it can perform work. Thermal energy can be obtained from other forms of energy, and heat can also be converted into other forms of energy. For instance, when water is heated in a covered pot, it changes into steam. As the steam pressure builds up, it lifts and rattles the lid. Here, thermal energy is converted into mechanical energy. On a cold winter day, rubbing our palms together creates friction, which produces heat. In this process, mechanical energy is converted into thermal energy.

Temperature

Temperature is related to the random motion of atoms and molecules in a substance. It is proportional to the motion that carries atoms and molecules from one place to another.

Unit of Temperature

In the International System of Units (SI), the unit of temperature is the Kelvin, though the older Celsius scale — still in everyday use — was historically the more common reference. One degree Celsius is defined as one-hundredth part of the temperature difference between melting ice and boiling water under normal pressure. The melting point of ice is taken as 0°C and the boiling point of water is taken as 100°C. The definition of the Kelvin is given based on the triple point of water.

The specific temperature and pressure at which water coexists in all three states—namely as ice, water, and water vapor—is called the triple point of water. The temperature of this triple point is taken as 273.16 K.

📌Remember, the melting point of ice is 273.15 K ( not 273.16 K) and the boiling point of water is 373.15 K. Therefore, the temperature difference between the melting point of ice and the boiling point of water is 100 K.

Difference Between Heat and Temperature

2. Temperature Scales

We use different scales to measure temperature. The three temperature scales widely used today are Celcius, Fahrenheit, and Kelvin.

Historical Context:

• Fahrenheit (1724): The first of the three, it introduced the idea of using fixed reference points.
• Celsius (1742): Inspired by Fahrenheit, Anders Celsius created a 100-step scale (fun fact: his original scale was upside down, with 0°C as the boiling point!).
• Kelvin (1848): Lord Kelvin kept the exact same degree size as Celsius, but shifted the starting point all the way down to absolute zero (0 K).

📌Memorize this relation carefully — SSC board exams frequently feature conversion problems between these scales.

$\frac{T_C}{100} = \frac{T_F - 32}{180} = \frac{T_K - 273.15}{100}$

$\text{or, } \frac{T_C}{5} = \frac{T_F - 32}{9} = \frac{T_K - 273.15}{5}$

Here, T_C is temperature in celsius scale, T_F is temperature in Fahrenheit scale, and T_K is temperature in Kelvin scale.

Problem: An ice cube of 120g mass is at -5°C. Find out the temperature of the piece of ice in Fahrenheit scale. SSC: M. B. '20 

Solution: 

Given,

Temperature in celsius scale, T_C = -5°C

Temperature in fahrenheit scale, T_F = ?

We know that, $\frac{T_C}{5} = \frac{T_F - 32}{9}$ $\text{ or, } T_F = \frac{T_C \times 9} {5} + 32$

$\text{ or, } T_F = \frac{-5 \times 9} {5} + 32 = -9 + 32 = 23°F$

Challenge Yourself: Practice Problems to Solidify the Concept

1. The highest officially recorded temperature in Bangladesh was 113.2°F on May 15, 1972.
   1. What is this temperature on the Celsius scale? Answer: 45.1°C
   2. What is this temperature on the Kelvin scale? Answer: 318.25K

2. At what temperature is the Fahrenheit scale reading equal to twice that of the Celsius scale? Answer: 320°F

3. What Fahrenheit temperature is half the value of the corresponding Celsius temperature? Answer: -12.3°F