1.0 Concepts of Heat and Temperature
While often used interchangeably in daily conversation, Heat and Temperature are distinct physical concepts. Heat is a form of energy that flows from a body at a higher temperature to a body at a lower temperature, whereas temperature is a measure of the degree of "hotness" or "coldness" of an object.
Heat vs. Temperature
| Feature | Heat Energy | Temperature |
|---|---|---|
| Definition | Sum of internal energies of molecules. | Average kinetic energy of molecules. |
| S.I. Unit | Joule (J) | Kelvin (K) |
| Instrument | Calorimeter | Thermometer |
1.1 Units of Heat Energy
Apart from the S.I. unit (Joule), heat is frequently measured in Calories, especially in the context of nutrition and calorimetry.
- Calorie (cal): The amount of heat energy required to raise the temperature of $1\,g$ of water by $1^\circ C$.
- Kilocalorie (kcal): $1\,kcal = 1000\,cal$.
Mechanical Equivalent of Heat
$$1 \text{ calorie} \approx 4.186 \text{ Joules}$$
For numerical calculations, we often use **4.2 J**.
1.2 Temperature Scales
There are three main scales used to measure temperature: Celsius ($^\circ C$), Fahrenheit ($^\circ F$), and Kelvin ($K$). The Kelvin scale is known as the Absolute Scale of temperature.
The temperature of $0\,K$ is called Absolute Zero. It is theoretically the lowest possible temperature where all molecular motion stops.
Remember: $0\,K = -273.15^\circ C$. You can never have a negative temperature on the Kelvin scale!
The normal temperature of the human body is $98.6^\circ F$. Convert this temperature into Celsius ($^\circ C$).
Solution:
1. Formula: $\frac{C}{5} = \frac{F - 32}{9}$
2. Substitution: $\frac{C}{5} = \frac{98.6 - 32}{9}$
3. Calculation: $\frac{C}{5} = \frac{66.6}{9} \Rightarrow C = 5 \times 7.4 = \mathbf{37^\circ C}$
Final Answer: Normal body temperature is $37^\circ C$.
Lord Kelvin, who the Kelvin scale is named after, calculated the absolute zero point by studying the relationship between the volume and temperature of gases. He realized that if the trend continued, a gas would reach "zero volume" at $-273^\circ C$!
2.0 Thermal Expansion
Most substances—whether solid, liquid, or gas—expand when heated and contract when cooled. This happens because heating increases the Kinetic Energy of the molecules, causing them to vibrate more vigorously and take up more space. This phenomenon is known as Thermal Expansion.
Three Types of Expansion in Solids
- Linear Expansion: Increase in the length of a solid.
- Superficial Expansion: Increase in the area of a solid.
- Cubical Expansion: Increase in the volume of a solid.
Note: Liquids and Gases only show Cubical (Volume) Expansion as they do not have a fixed shape.
2.1 Anomalous Expansion of Water
Water shows a very unique and "anomalous" behavior. Generally, liquids contract on cooling, but water contracts only until it reaches 4°C. If cooled further from 4°C to 0°C, it actually expands!
Importance for Aquatic Life
In cold climates, as the temperature of a lake falls, the water at the top reaches 4°C, becomes densest, and sinks. This continues until the entire lake is at 4°C. When the surface water cools below 4°C, it becomes less dense and stays on top, eventually freezing into ice. This ice acts as an insulator, keeping the water below at 4°C and allowing fish to survive.
Coefficient of Linear Expansion ($\alpha$)
$$\alpha = \frac{\Delta L}{L_0 \times \Delta T}$$
Where: $\Delta L$ = Change in length, $L_0$ = Original length, $\Delta T$ = Change in temperature.
Unit: per °C or per K ($^\circ C^{-1}$ or $K^{-1}$)
Railway tracks are never laid in one continuous piece. Small gaps are left between the rails to allow for expansion during summer. If these gaps weren't there, the tracks would buckle and cause train accidents!
An iron rod of length 2 m is heated from 20°C to 120°C. If the coefficient of linear expansion of iron is $1.2 \times 10^{-5} \, ^\circ C^{-1}$, calculate the increase in its length.
Solution:
1. Given: $L_0 = 2\,m$, $\Delta T = 120 - 20 = 100\,^\circ C$, $\alpha = 1.2 \times 10^{-5}\,^\circ C^{-1}$.
2. Formula: $\Delta L = L_0 \times \alpha \times \Delta T$
3. Calculation: $\Delta L = 2 \times (1.2 \times 10^{-5}) \times 100$
4. $\Delta L = 2 \times 1.2 \times 10^{-3} = 2.4 \times 10^{-3}\,m = \mathbf{2.4\,mm}$.
Final Answer: The increase in length is $2.4\,mm$.
The Eiffel Tower can be up to 15 cm taller in the summer than in the winter! Because it is made of puddled iron, the metal expands as it soaks up the sun's heat, causing the entire structure to grow.
3.0 Change of State
Matter can change from one state to another (Solid, Liquid, or Gas) by either absorbing or releasing heat. During this transition, a very interesting phenomenon occurs: the temperature of the substance remains constant even though heat is being supplied or removed. This heat is used to break or form the bonds between molecules.
Latent Heat (Hidden Heat)
The heat energy exchanged during a change of state without any change in temperature is called Latent Heat. It is divided into two main categories:
- Latent Heat of Fusion: Heat required to change a substance from Solid to Liquid at its melting point.
- Latent Heat of Vaporization: Heat required to change a substance from Liquid to Gas at its boiling point.
Formula for Latent Heat
$$Q = m \times L$$
Where: $Q$ = Total heat absorbed/released, $m$ = Mass, $L$ = Specific Latent Heat.
Unit: $J/kg$ or $cal/g$
3.1 Specific Latent Heat Values
Water and Ice have remarkably high specific latent heat values, which has a significant impact on our environment:
- Specific Latent Heat of Ice ($L_f$): $336,000\,J/kg$ (or $80\,cal/g$). This high value explains why snow melts slowly and why lakes don't freeze instantly.
- Specific Latent Heat of Steam ($L_v$): $2,260,000\,J/kg$ (or $540\,cal/g$). This is why steam causes much more severe burns than boiling water at the same temperature.
Do not confuse these two!
1. Evaporation: Occurs at all temperatures, from the surface, and causes cooling.
2. Boiling: Occurs only at a fixed temperature (Boiling Point), from the entire bulk of the liquid, and doesn't cause cooling.
How much heat energy is required to melt $2\,kg$ of ice at $0^\circ C$ to water at $0^\circ C$? (Specific latent heat of ice = $336\,kJ/kg$)
Solution:
1. Given: Mass ($m$) = $2\,kg$, $L_f = 336 \times 10^3\,J/kg$.
2. Formula: $Q = m \times L_f$
3. Calculation: $Q = 2 \times 336 \times 10^3$
4. $Q = 672 \times 10^3 = \mathbf{672,000\,J}$ (or $672\,kJ$).
Final Answer: Total heat required is $672\,kJ$.
During a hailstorm, after the hail stops falling, the surroundings become very cold. This is because the ice (hail) absorbs a huge amount of latent heat from the air to melt into water, significantly lowering the air temperature.
4.0 Transmission of Heat
Heat energy naturally moves from a region of higher temperature to a region of lower temperature. There are three distinct modes through which this transfer takes place: Conduction, Convection, and Radiation.
The Three Modes of Transfer
- Conduction: Transfer of heat in solids through molecular vibrations without the actual movement of particles.
- Convection: Transfer of heat in fluids (liquids and gases) through the actual movement of the particles themselves (convection currents).
- Radiation: Transfer of heat that does not require a medium. It travels in the form of electromagnetic waves (e.g., heat from the Sun).
4.1 Convection in Nature: Sea and Land Breezes
Convection currents in the atmosphere are responsible for local winds near coastal areas. These occur because land heats up and cools down much faster than water due to its lower specific heat capacity.
- Sea Breeze (Day): Land gets hot; air above it rises. Cooler air from the sea rushes in to take its place.
- Land Breeze (Night): Land cools faster; air above the sea is now warmer and rises. Cooler air from the land rushes toward the sea.
Rate of Heat Flow (Conduction)
$$Q = \frac{K \cdot A \cdot (T_1 - T_2) \cdot t}{d}$$
Where: $K$ = Thermal conductivity, $A$ = Area, $T_1 - T_2$ = Temp difference, $d$ = Thickness.
Air is a very poor conductor of heat. This is why we wear woolen clothes in winter. The wool traps a layer of air, preventing our body heat from escaping via conduction to the cold surroundings.
Why are the heating elements of a room heater placed at the bottom, while the cooling unit of an AC is placed at the top?
Solution:
1. Heater: Hot air is less dense and rises. Placing the heater at the bottom allows convection currents to warm the entire room.
2. AC: Cold air is denser and sinks. Placing the AC at the top allows the cold air to fall and cool the lower parts of the room efficiently.
Final Answer: This setup ensures efficient circulation of air through convection currents.
The Thermos Flask is designed to stop all three modes of heat transfer! The vacuum stops conduction and convection, while the silvered inner walls reflect heat back to prevent radiation loss.
5.0 Energy Sources and Conservation
Energy is the capacity to do work. In our modern world, the demand for energy is ever-increasing. We categorize our energy sources based on their availability and impact on the environment into Renewable and Non-Renewable sources.
Classification of Energy Sources
- Non-Renewable Sources: Sources that are depleted over time and cannot be easily replaced (e.g., Coal, Petroleum, Natural Gas). These are often called Fossil Fuels.
- Renewable Sources: Sources that are inexhaustible and are naturally replenished (e.g., Solar, Wind, Hydroelectric, Geothermal, and Biomass).
5.1 The Greenhouse Effect
The excessive use of fossil fuels releases gases like Carbon Dioxide ($CO_2$) and Methane ($CH_4$). These gases trap the Sun's heat within the Earth's atmosphere, leading to a rise in global temperatures known as Global Warming.
Efficiency of an Energy System
$$\eta = \frac{\text{Useful Output Energy}}{\text{Total Input Energy}} \times 100$$
Where: $\eta$ (eta) represents Efficiency. No system is ever 100% efficient due to heat loss.
5.2 Energy Degradation
When energy is converted from one form to another, a part of it is always converted into a non-useful form (usually heat due to friction or resistance). This "useless" energy is dissipated into the surroundings and cannot be recovered. This is called the Degradation of Energy.
Energy can neither be created nor destroyed; it can only be transformed from one form to another. While the total energy of an isolated system remains constant, the useful energy always decreases over time.
An electric motor consumes $1000\,J$ of electrical energy to lift a weight, performing $800\,J$ of useful work. Calculate the efficiency and the energy degraded.
Solution:
1. Efficiency ($\eta$): $\frac{800}{1000} \times 100 = \mathbf{80\%}$.
2. Energy Degraded: Total Input - Useful Output = $1000\,J - 800\,J = \mathbf{200\,J}$.
Final Answer: The efficiency is $80\%$ and $200\,J$ of energy is wasted as heat/sound.
The Sun is the ultimate source of almost all energy on Earth! Even fossil fuels like coal are essentially "buried sunshine"—stored solar energy from plants that lived millions of years ago.