Heat

Detailed Notes

• Latent heat and change of state.
• Regelation and anomalous behaviour of water.
• Dew point, humidity and relative humidity.
• Specific heat capacity and heat exchange.

Latent Heat – Heating Ice

Figure 5.1 – Latent heat experiment

• When ice is heated, it starts melting. The mixture remains at 0°C until all the ice melts.
• Even though heat is supplied, the temperature does not rise during the change of state.
• The absorbed heat is used to weaken bonds and transform the solid into liquid.

Latent Heat of Fusion

• The constant temperature at which ice changes into water is called the melting point of ice.
• The heat energy absorbed at constant temperature during transformation of solid into liquid is called as latent heat of fusion.
• Specific latent heat of fusion is the heat absorbed at constant temperature by unit mass of a solid to convert it into liquid phase.

Latent Heat of Vaporization

• After all ice becomes water, the temperature rises from 0°C to 100°C.
• At 100°C, water changes into steam while its temperature remains constant.
• The heat absorbed at constant temperature during liquid-to-gas transformation is called as latent heat of vaporization.
• Specific latent heat of vaporization is the heat absorbed at constant temperature by unit mass of a liquid to convert into gaseous phase.

Temperature vs Time Graph

Figure 5.2 – Temperature vs Time Graph

• AB: Ice changes into water at 0°C. Heat is absorbed, but temperature remains constant.
• BC: Water temperature rises from 0°C to 100°C.
• CD: Water changes into steam at 100°C. Temperature again remains constant.

Regelation

Figure 5.3 – Regelation

• A metal wire with equal weights is placed over a slab of ice. The wire gradually penetrates the ice, but the slab does not break.
• The phenomenon in which ice converts into liquid due to applied pressure and then reconverts into ice when pressure is removed is called as regelation.
• Pressure lowers the melting point of ice below 0°C. When pressure is removed, the melting point is restored to 0°C.

Anomalous Behaviour of Water

Figure 5.4 – Volume and temperature of water

• Normally, liquids expand on heating and contract on cooling. Water behaves differently between 0°C and 4°C.
• When water is heated from 0°C to 4°C, it contracts. At 4°C its volume is minimum.
• Above 4°C, water expands normally. Therefore, water has maximum density at 4°C.

Construction

Figure 5.5 – Hope’s apparatus

• Hope’s apparatus has a cylindrical container with a flat bowl around its middle.
• Two thermometers are fitted above and below the flat bowl: T₂ above and T₁ below.
• Water is filled in the cylinder and a freezing mixture of ice and salt is placed in the flat bowl.

Working

Figure 5.6 – Time–Temperature Graph

• Initially T₁ and T₂ are the same. As cooling starts, T₁ in the lower part falls faster than T₂.
• When T₁ reaches 4°C, it remains almost steady for some time. Water at 4°C has maximum density and moves downward.
• Below 4°C, water expands and its density decreases, so it moves upward. T₂ reaches 0°C first.

Aquatic Life in Cold Regions

Figure 5.7 – Aquatic animals in cold regions

• In cold regions, the upper layer of a water body freezes and forms an ice layer.
• Water at 4°C has maximum density and moves downward. Water below the ice remains liquid.
• Therefore aquatic plants and animals can survive even when atmospheric temperature goes below 0°C.
• In winter, expansion of freezing water can also make water-supply pipes break and rocks crack.

Dew Point

• For a given volume of air at a particular temperature, there is a limit to the amount of water vapour it can contain.
• When unsaturated air is cooled, a temperature is reached at which it becomes saturated with vapour.
• This temperature is called as dew point temperature.
• When air cools further, excess water vapour changes into tiny water droplets.

Humidity and Saturated Air

• The moisture present in the atmosphere is called as humidity.
• When air contains the maximum possible amount of water vapour at a given temperature, it is said to be saturated with vapour.
• If the vapour content is less than the maximum limit, the air is unsaturated.
• At 40°C, air can contain about 49 g of water vapour per kilogram of dry air without condensation; at 20°C it can contain about 14.7 g.

Relative Humidity

• The ratio of actual water vapour content to the amount required to saturate the same volume of air at the same temperature is called as relative humidity.
• At the dew point, relative humidity is 100%.
• If relative humidity is more than 60%, we feel the air is humid. If it is less than 60%, we feel the air is dry.
• A white trail behind an aeroplane can last longer when surrounding relative humidity is high.

Unit of Heat and Joule

• The SI unit of heat is joule (J). The CGS unit is calorie (cal).
• One calorie is the heat needed to raise 1 g of water by 1°C from 14.5°C to 15.5°C.
• One kilocalorie is the heat needed to raise 1 kg of water by 1°C over the same interval.
• 1 kcal = 1000 cal and 1 cal = 4.18 J.

Specific Heat Capacity – Experiment

Figure 5.8 – Specific heat capacity of metals

• Equal-mass iron, copper and lead spheres are heated to 100°C and placed on a thick wax slab.
• Iron goes deepest into the wax, lead the least, and copper an intermediate distance.
• This shows that different substances absorb different amounts of heat for the same rise in temperature.

Specific Heat

• The amount of heat energy required to raise the temperature of a unit mass of an object by 1°C is called as specific heat.
• Specific heat is denoted by c.
• SI unit: J/(kg°C).
• CGS unit: cal/(g°C).

Figure 5.9 – Specific heat capacity of some substances

Heat Absorbed / Heat Lost

• If the specific heat is c, mass is m, and temperature rises by ΔT, the heat energy absorbed is given by the relation below.
• If the temperature decreases by ΔT, the heat energy lost is also equal in magnitude.

Heat Exchange and Calorimeter

Figure 5.10 – Box of heat resistant material

• When a hot and cold object exchange heat, the cold object's temperature rises and the hot object's temperature falls until both reach the same temperature.
• In an isolated system, heat energy lost by the hot object equals heat energy gained by the cold object. This is called as the principle of heat exchange.
• In the mixing method, a hot solid is placed in water in a calorimeter until the solid, water and calorimeter reach the same temperature.

Heat Energy

Question: How much heat energy is necessary to raise the temperature of 5 kg of water from 20°C to 100°C?

• Given: m = 5 kg, c = 1 kcal/(kg°C), ΔT = 100 − 20 = 80°C.
• Use: Q = m × c × ΔT.
• Q = 5 × 1 × 80 = 400 kcal.

Heat Exchange – Final Temperature

A 100 g copper sphere at 100°C is placed in 195 g water at 20°C in a 50 g copper calorimeter.

• Specific heat of copper and calorimeter = 0.1 cal/(g°C).
• Heat lost by copper sphere = heat gained by water + heat gained by calorimeter.
• Using the heat-exchange equation gives the final temperature T = 23.8°C.