Samacheer Kalvi 9th Science Heat Exercise Solutions

Heat is a form of energy that flows from a body at higher temperature to a body at lower temperature. It is measured in joules (J) in the SI system. Heat transfer continues until both bodies reach the same temperature (thermal equilibrium). Heat depends on the mass, specific heat capacity, and temperature change of the substance.

Specific heat capacity is the amount of heat required to raise the temperature of 1 kg of a substance by 1 K (or 1°C). The formula is c = Q/(mΔT), and its SI unit is J/(kg·K). Every substance has a unique specific heat capacity — water has one of the highest at 4186 J/(kg·K), while metals like copper have much lower values around 385 J/(kg·K).

Latent heat is the heat energy absorbed or released during a change of state without any change in temperature. There are two types: latent heat of fusion (solid to liquid) and latent heat of vaporisation (liquid to gas). For example, ice at 0°C absorbs 3.34 × 10⁵ J/kg to become water at 0°C, and water at 100°C absorbs 2.26 × 10⁶ J/kg to become steam at 100°C.

Water has a very high specific heat capacity (4186 J/kg·K). It can absorb a large amount of heat from the engine without a significant rise in its own temperature, making it an effective coolant. Additionally, water is readily available, inexpensive, and has a high boiling point, which allows it to function efficiently in the cooling system of an engine.

Thermal expansion is the increase in the dimensions (length, area, or volume) of a substance when it is heated. Solids expand least, liquids more, and gases the most for the same temperature change. Everyday examples include the expansion of railway tracks in summer, the cracking of glass when hot water is poured on it, and the expansion of mercury in a thermometer.

Heat is the total energy of molecular motion in a substance, measured in joules (J), and depends on mass, specific heat, and temperature difference. Temperature is the measure of the average kinetic energy of molecules, measured in °C, K, or °F, and indicates how hot or cold a body is. A large iceberg at 0°C has more heat than a cup of boiling water, but the cup has a higher temperature.

Heat can be transferred by three distinct modes, each operating under different conditions:

Conduction:

• Requires a material medium (typically a solid).
• Heat is transferred through molecular vibrations without actual movement of the particles from their positions.
• The molecules at the hot end vibrate more vigorously and transfer energy to neighbouring molecules.
• Example: A metal spoon left in a hot pot becomes hot at its far end.

Convection:

• Requires a fluid medium (liquid or gas).
• Heated fluid becomes less dense and rises, while cooler, denser fluid sinks — creating convection currents.
• This is a bulk movement of particles carrying heat energy.
• Example: Boiling water where hot water rises from the bottom and cool water descends; sea breeze and land breeze.

Radiation:

• Does not require any medium — heat travels as electromagnetic waves (infrared radiation).
• Can travel through vacuum (the Sun's heat reaches Earth through the vacuum of space).
• Dark, rough surfaces are good absorbers and radiators; light, shiny surfaces are good reflectors.
• Example: The warmth you feel from a campfire, or sunlight reaching Earth.

Water has an exceptionally high specific heat capacity of 4186 J/(kg·K), which is significantly higher than that of land (approximately 800–1000 J/(kg·K) for soil and rock). This large difference has important consequences for coastal climates:

• During the day, the Sun heats both land and sea. Because water requires much more heat to raise its temperature, the sea warms up slowly and keeps the air above it cool. The cool sea breeze blows towards the land, moderating the coastal temperature.
• During the night, the land cools rapidly because of its low specific heat, while the sea retains its heat for much longer. The warm air over the sea rises and the warmer sea breeze continues to moderate the coastal temperature.
• Seasonally, the same effect operates over longer periods. In summer, the ocean absorbs heat and keeps coastal regions cooler than inland areas. In winter, the ocean slowly releases stored heat and keeps coastal regions warmer than inland areas.
• In contrast, inland (interior) regions experience extreme temperatures — very hot in summer and very cold in winter — because land heats up and cools down rapidly due to its low specific heat.

This moderating effect is why cities like Chennai and Mumbai have less temperature variation throughout the year compared to cities like Delhi or Nagpur.

The concept of specific heat capacity has several practical applications in daily life and engineering:

1. Water as a coolant in engines and radiators: Water's high specific heat (4186 J/kg·K) allows it to absorb large amounts of heat from engines without a significant temperature rise, making it an ideal coolant in car radiators and industrial cooling systems.

2. Cooking utensils made of metals: Metals like aluminium and copper have low specific heat capacities, so they heat up quickly when placed on a flame, enabling efficient cooking.

3. Handles of cooking utensils made of wood or plastic: Wood and plastic have high specific heat capacities and are poor conductors of heat, so they do not heat up quickly and remain safe to touch even when the metal part is hot.

4. Coastal climate moderation: As explained above, the high specific heat of water moderates the climate of coastal regions compared to inland areas.

5. Use of water in hot water bottles: Water retains heat for a long time due to its high specific heat, making it suitable for hot water bottles used for warmth in winter.

6. Thermal insulation in buildings: Materials with high specific heat are used in building walls to slow down temperature changes, keeping buildings cooler in summer and warmer in winter.

Principle: Heat lost by hot body = Heat gained by cold body (law of conservation of energy). This is the principle of calorimetry.

Procedure: 1. Weigh the empty calorimeter with stirrer and note its mass (m₁). 2. Fill the calorimeter with a known mass of water (m₂) and note the initial temperature (T₁) using a thermometer. 3. Heat a solid of known mass (m₃) to a known high temperature (T₂) using a water bath or steam heater. 4. Quickly transfer the hot solid into the calorimeter and stir the mixture continuously. 5. Note the final steady temperature (T₃) when the thermometer reading becomes constant.

A typical heating curve for ice at –20°C to steam above 100°C shows five distinct regions:

1. Ice heating (–20°C to 0°C): Temperature rises steadily as heat is used to increase the kinetic energy of ice molecules. The formula is Q = m × c_ice × ΔT, where c_ice ≈ 2100 J/(kg·K). The slope of this region depends on the specific heat of ice.

2. Ice melting (at 0°C): Temperature remains constant as heat is used to break intermolecular bonds and change ice to water. This is latent heat of fusion: Q = m × Lf, where Lf = 3.34 × 10⁵ J/kg. The flat portion of the graph represents this phase change.

3. Water heating (0°C to 100°C): Temperature rises as water absorbs heat: Q = m × c_water × ΔT, where c_water = 4186 J/(kg·K). This region has a gentler slope than ice heating because water has a higher specific heat capacity than ice.

4. Water boiling (at 100°C): Temperature again remains constant as heat converts water to steam. This is latent heat of vaporisation: Q = m × Lv, where Lv = 2.26 × 10⁶ J/kg. Note that Lv is much larger than Lf, so this flat portion is longer on the graph.

5. Steam heating (above 100°C): Temperature rises again: Q = m × c_steam × ΔT, where c_steam ≈ 2010 J/(kg·K).

The flat portions of the graph represent change of state where all energy goes into breaking bonds rather than increasing temperature. The total heat required to go from ice at –20°C to steam at 100°C+ is the sum of all five steps.

Heat lost by iron = Heat gained by water