The relationship between density and temperature is given by: $$ density = \frac{mass}{Volume} $$ $${d_1} = \frac{M}{V_1} $$ $$ M = {d_1}{V_1} $$ $$ {d_2} = \frac{M}{V_2} $$ $$ M = {d_2}{V_2} $$ Equating both equations where M is a constant $$ {d_1}{V_1} = {d_2}{V_2} $$ $$ \frac{V_1}{V_2} = \frac{d_2}{d_1} $$ $$ \text{But, }{V_2} = \gamma × {V_1} × {∆\theta} + {V_1} $$ $$ {V_2} = {V_1}(1 + {\gamma}{∆\theta}) $$ $$ \frac{V_2}{V_1} = 1 + {\gamma}{∆\theta} $$ $$ \frac{V_2}{V_1} = \frac{d_1}{d_2} = 1 + {\gamma}{∆\theta} $$ $$ {d_1} = {d_2}({1 + {\gamma}{∆\theta}}) $$ $$ \text{where, }{d_1} = \text{density at lower temp.} $$ $$ {d_2} = \text{temperature at higher temp.} $$ Note: At lower temperature, a liquid is more dense than at a higher temperature.

Melting: This is the process where a solid turns into a liquid due to an increase in temperature. The heat provides enough energy to overcome the forces holding the particles in a fixed arrangement.

Evaporation: This process involves the transformation of a liquid into a gas, typically occurring at the liquid's surface. It happens at temperatures below the boiling point, where particles gain enough energy to escape the liquid phase.

Sublimation: Sublimation occurs when a substance transitions directly from a solid to a gas without passing through the liquid phase. This happens when the substance absorbs enough heat energy.

Freezing: The reverse of melting, freezing is the process where a liquid turns into a solid. It occurs when the temperature decreases, causing the particles to lose energy and form a more ordered structure.

Condensation: Condensation is the transformation of a gas into a liquid. It occurs when a gas loses heat energy and its particles slow down, coming together to form a liquid.

Deposition: Deposition is the direct transition of a gas to a solid without passing through the liquid phase. This happens when the gas loses energy, causing the particles to slow down and come together to form a solid.

Evaporation: This process involves the transformation of a liquid into a gas, typically occurring at the liquid's surface. It happens at temperatures below the boiling point, where particles gain enough energy to escape the liquid phase.

Boiling: Boiling is the rapid conversion of a liquid into a gas throughout the entire volume of the liquid. It occurs at the substance's boiling point and involves the formation of vapor bubbles within the liquid.

Heat is transferred from a hot body to a cold body. The processes involved in the transfer of heat include:

1. Conduction
2. Convection
3. Radiation

Conduction is the process of heat transfer through direct contact between particles. It occurs in solids, where vibrating particles transfer kinetic energy to neighboring particles.

Thermal conductivity is a property that quantifies how well a material conducts heat. Materials with high thermal conductivity transfer heat more efficiently than those with low thermal conductivity. Examples of good conductors are copper, aluminum, iron, etc. Most non-metals like plastics, glass and water are poor conductors of heat. Poor conductors of heat are called insulators.

1. Applications in Cooking Utensils: Cooking utensils, such as metal pans, utilize high thermal conductivity to distribute heat evenly. This ensures efficient cooking as heat is quickly transferred from the stove to the food.
2. Applications in Use of Rugs on Floor: Rugs on the floor can act as insulators, reducing heat conduction between the feet and a cold floor. The material and thickness of the rug influence its effectiveness in providing thermal comfort. Tiles are better conductors of heat hence they feel colder to touch.
3. Applications in Use of Cloth to Keep Warm: Clothing made from materials with low thermal conductivity, like wool or fleece, helps trap body heat and insulate against the colder surrounding environment, keeping individuals warm.
4. Applications in Home Cooling System: Insulating materials with low thermal conductivity are used in the construction of walls and roofs to minimize heat transfer between the interior and exterior of a building. Additionally, materials with high thermal conductivity, such as metal fins in air conditioning systems, facilitate efficient heat dissipation.

Convection is the process of heat transfer through the movement of fluids. In liquids and gases, warmer regions become less dense and rise, while cooler, denser regions sink. This creates a continuous circulation of the fluid, transferring heat from one place to another.

This is a practical application of convection in nature Land and sea breezes are local convection currents influenced by temperature differences between land and water. During the day, land heats up faster than the sea, causing air over the land to rise. This creates a low-pressure area, and cooler air from the sea moves in to replace it, creating a sea breeze. At night, the process reverses, leading to a land breeze.

1. Heating a Room: Convection is utilized in heating systems where warm air rises, creating a circulation that warms the entire room.
2. Cooling Systems: Air conditioning systems use convection to cool indoor spaces. Warm air is drawn in, cooled, and then circulated back into the room.
3. Cooking: Convection ovens use a fan to circulate hot air, ensuring even cooking by transferring heat to the food more efficiently.
4. Ocean Currents: Large-scale convection currents in the ocean influence climate patterns and marine ecosystems.

Radiation is the process of heat transfer through electromagnetic waves, without the need for a medium. It can occur in a vacuum and involves the emission, transmission, and absorption of energy in the form of electromagnetic waves.

Various instruments, such as Geiger-Muller counters and scintillation detectors, are used to detect and measure different types of radiation. These devices help monitor and ensure safety in environments where radiation may be present.

1. Dull and Polished Surfaces: Radiation plays a role in the interaction between surfaces and heat. Dull surfaces absorb more radiation, while polished or reflective surfaces reflect more, influencing temperature variations.
2. Color of Clothes: Dark-colored clothes absorb more radiation than light-colored ones. This property is utilized for personal comfort in choosing clothing based on weather conditions.

A thermos flask is designed to minimize heat transfer, ensuring that the contents inside remain at a constant temperature. Several mechanisms contribute to heat conservation:

1. Double-Walled Construction: Thermos flasks have a double-walled structure with a vacuum or insulating material between the walls. This reduces heat transfer by conduction as there's no direct contact between the inner and outer surfaces.
2. Reflective Surfaces: The inner surfaces of the thermos flask are often coated with reflective materials to minimize heat radiation. This helps prevent the emission of infrared radiation from the contents.
3. Airtight Seal: The flask is designed with an airtight seal to prevent the exchange of air between the inside and outside. This minimizes heat transfer by convection, as there is no movement of air to carry away or introduce heat.
4. Low Emissivity Coating: Some thermos flasks feature a low emissivity coating on the inner surface, reducing the emission of thermal radiation and improving heat retention.
5. Insulating Materials: The walls of the thermos are often made of materials with low thermal conductivity, such as glass or certain types of plastic. This further reduces heat transfer through the walls.