Solutions-Class 10-Science & Technology-1-Chapter-5-Heat-Maharashtra Board

1. The amount of water vapour in air is determined in terms of its absolute humidity.

2. If objects of equal masses are given equal heat, their final temperature will be different. This is due to difference in their different specific heat capacity.

3. During transformation of liquid phase to solid phase, the latent heat is latent heat of fusion.

• Most of the substances expand on heating and contract on cooling.
• Whereas, from the graph, it is clearly visible that water shows a distinct and peculiar behavior between 0^oc to 4^o
• If the temperature of water is raised from 0°C to 10°C, its volume goes on decreasing in the range 0°C to 4°C. It is minimum at 4°C.
• The volume of water goes on increasing in the range 4°C to 10°C Thus after 4^oc, it shows the normal behavior of expansion as is shown by other substances.
• In general, when a substance is heated, its volume goes on increasing with temperature. Thus, in the range 0°C to 4°C, behaviour of water is different from other substances. This behavior of water between 0^oc to 4^oc is known as anomalous behavior of water.

Specific heat capacity of a body is the amount of heat energy required to raise the temperature of unit mass of that body through 1^oC (or 1 K). It is given as
\(s=\frac{∆Q}{∆T}×m\)
where,
ΔQ=Amount of heat energy supplied

ΔT=Rise in temperature

m=Mass of the body

Experiment to prove different substances have different specific heat capacities:

• Take three spheres, each will have different material but equal mass. Let take sphere of iron, copper and lead of equal mass and put them in boiling water for some time.
• Then, take them out of the water and measure their temperature. All of them will be at temperature 100^o
• Now, put them immediately on the thick slab of wax. Note the depth that each of the spheres goes into the wax.
• The spheres which absorbs more heat from the water will give more heat to wax. More wax will thus melt and the spheres will go deeper in the wax.
• It will be observed that the iron spheres goes deepest into the wax. Lead spheres goes the least and copper spheres goes to in-between depth.
• This shows that for equal rise in temperature, the three spheres have absorbed different amounts of heat.
• This means that the property which determines the amount of heat absorbed by a sphere is different for the three spheres. This property is called the specific heat capacity.

The amount of heat energy required to raise the temperature of a unit mass of an object by 1°C is called the specific heat capacity or simply specific heat of the object.

While deciding the unit for heat (which is calorie), the temperature interval chosen is 14.5^oC-15.5^oC.
If we heat 1 kg of water by 1°C in different temperature range than 14.5°C to 15.5°C, the amount of heat required will be slightly different.

It is, therefore, essential to define a specific temperature range while defining the unit of heat.

• In the given graph, line AB represents conversion of ice into water at constant temperature.
• When ice is heated, it melts at 0^oC and converts into water maintaining constant temperature of 0^o
• During this transition, the ice absorbs heat energy. This heat energy is utilised for weakening the bonds between the atoms or molecules in the ice to transform itself into liquid.
• This constant temperature, at which the ice converts into water is called the melting point of ice.
• Also, This heat energy absorbed by ice, at constant temperature, to convert it into liquid is called the latent heat of fusion.
• Line BC in the graph represents rise in temperature of water from 0^oC to 100^o
• Once all the ice is transformed into water, the temperature of water starts rising. It increases upto 100^o The heat energy is absorbed by water at this temperature and is used to break the bonds between molecules of the liquid and convert the liquid into gaseous state.
• Thereafter, even though heat energy is supplied to water, its temperature does not rise. Thus, during transformation from liquid phase to gas phase, heat energy is absorbed by the liquid, but its temperature does not change.
• The constant temperature at which the liquid transforms into gaseous state is called the boiling point of the liquid.
• The heat energy absorbed at constant temperature during transformation of liquid into gas is called the latent heat of vaporization.

• The anomalous behaviour of water is that it contracts from 0^oC to 4^oC and beyond 4^oC it expands. Thus, the density of water is maximum at 4^o
• When the surrounding temperature falls, the water in oceans and rivers cools down and say the temperature of whole water reaches 4^o
• Thus, the water reaches its maximum density at this temperature.
• Below this temperature (4^oC), the water layer on the surface expands due to anomalous behaviour of water because of which it's density decreases.
• Thus, this colder layer remains on top  and converts into ice which acts as an insulator and does not allow the temperature of water layer below it to fall below 4^o
• In this way, When the water bodies (such as lakes; rivers; seas;), freeze in cold countries in winter, only the upper surface freezes to form ice.  Water below ice liveable temperature is maintained for the aquatic life, stays at 4ºC and hence, water animals can survive.

• If the temperature of unsaturated air is decreased, a temperature is reached at which the air becomes saturated with water vapour.
• In both the given processes, the temperature of the air near the surface of bottle or the leaves (in case of dew formation) decreases to dew point.
• Thus, the air becomes saturated with water vapour. As a result, water vapour converts or condenses into tiny water droplets which appears on the surface of bottle or leaves.

Water has the property of expanding below 4^oC, is called the anomalous behaviour of water. Thus, in cold regions when the temperature falls below 4^oC, the water content present in rocks expands. Due to this expansion of water or increase in volume of water, the rocks cracks.

• The amount of heat needed to change the state of unit mass of the body from solid to liquid or from liquid to gas without any change in temperature is called latent heat.
• When the latent heat is given off the body in liquid state, it will convert to solid state and the body in vapour state will transform to liquid state.
• This means the internal energy of the matter is reduced when latent heat is given off.

If a system of two objects is isolated from the environment by keeping it inside a heat resistant box, then no energy can leave the box or enter the box.

In this situation, heat energy lost by the hot object = heat energy gained by the cold object.

In due course, the two objects attain the same temperature. This is called Principal of Heat Exchange

Principle of heat exchange is used in the calorimetry method to determine the specific heat capacity of a substance.

According to the kinetic model, the total energy of a molecule is the sum of kinetic energy due to its motion (which depends on temperature) and its potential energy (which depends on the force of attraction between the molecules and the separation between them.

When a solid is heated, initially, its temperature increases. Here, the heat absorbed by substance is used in increasing the kinetic energy of the particles (atomic, molecules, etc.) of the substance as well as for doing work against the forces of attraction between them.

As the heating is continued, at a certain temperature (melting point), solid is converted into liquid. In this case, the temperature remains constant and the heat absorbed is used for weakening the bonds and conversion into liquid phase (liquid state). This heat is called the latent heat of fusion.

When a liquid is converted into the gaseous state, at the boiling point, the heat absorbed is used for breaking the bonds between the atoms or molecules. This heat is called the latent heat of vaporization.

Some solids, under certain conditions, are directly transformed into the gaseous phase. Here the heat is absorbed but the temperature remains constant. The absorbed heat is used for breaking the bonds between atoms or molecules. This heat is called the latent heat of sublimation.

In general, latent heat is the heat absorbed or given out by a substance during a change of state at constant temperature.

In transformations from liquid to solid, gas to liquid and gas to solid, latent heat is given out by the substance.

• On the basis of amount of water vapours present in the air, it can be either saturated or unsaturated.
• If the amount of water vapours exceeds the amount that the air can contain, then it is called saturated.
• If the amount of water vapour is less than the limit of the amount that air can contain then it is called unsaturated.
• We can determine whether the air is saturated with vapour or not in terms of relative humidity.
• If the relative humidity is 100%, the air is saturated with water vapour
• If the relative humidity is less than 100%, the air is not saturated with water vapour.

(i) Heat is transferred from the object at higher temperature to the object at lower temperature.

(ii) We learn the principle of heat exchange from this process.

(iii) Principle of heat exchange states that  If a system of two objects is isolated from the environment by keeping it inside a heat resistant box, then no energy can leave the box or enter the box. In this situation, heat energy lost by the hot object = heat energy gained by the cold object.In due course, the two objects attain the same temperature.

(iv) Specific heat of an object can be measured using this principle.

Given - m₁=100g, Δ T₁=3 °C, Δ T₂=5 °C, Q=Same

Specific heat capacity of a body is given as

Q=mc₁ Δ T₁= mc₂ ΔT₂

\(∴\frac{c_1}{c_2} = \frac{ΔT_2}{ΔT_1}=\frac{5°C}{3°C}=\frac{5}{3}\)

Thus c₁>c₂

Thus, specific heat capacity of body A is more than body B and by a factor of 5/3.

Given m₁=2 kg, ΔT₁=20 °C-0°C = 20 °C, c₁= 1 kcal/kg.°C, L₁ (ice)=80 kcal/kg, L₂ (vaporisation of ammonia)=341 cal/g = 341 kcal/kg m₂=?

Q₁ (heat lost by water) =m₁c₁ Δ T₁ + m₁L₁

= 2kg × 1 kcal/kg.°C × 20°C + 2kg × 80 kcal/kg

= 40+160=200 kcal

Q₂ (heat absorbed by ammonia) = m₂L₂ = m₂ × 341 kcal/kg

According to principle of heat exchange Q₁=Q₂

∴ 200 kcal = m₂ × 341 kcal/kg

∴ m₂ = 200/341 kg =0.5865 kg = 586.5 g

Given : m₁ = 150 g, ΔT₁=50°C-0°C=50 °C,
C_w=1 cal/g.°C, L₁ = 80 cal/g, L₂ = 540 cal/g,
ΔT₂ = 100°C-50°C = 50°C, m₂ = ?
Q₁ (heat absorbed by ice)= m₁L₁ = 150 g x 80 cal/g = 12000 cal

Q₂ (heat absorbed by water formed on melting of ice) = m₁ C_w ΔT₁

= 150 g x 1 cal/g.°C x 50°C = 7500 cal

Q₃ (heat given out by steam) = m₂ L₂ = m₂ x 540 cal/g

Q₄ (heat given out by water formed on condensation of steam)

= m₂ C_w ΔT₂ = m₂ x 1 cal/g.°C x 50°C = m₂ x 50 cal/g

According to the principle of heat exchange,
Q₁+Q₂= Q₃+Q₄
∴ 12000 cal +7500 cal = m₂ x 540 cal/g + m₂ x 50 cal/g
∴ 19500 cal = m₂ (540 +50) cal/g
∴ m_{2 =} 19500/590 = 33.05 g
33.05 g of steam is to be mixed.

Given: m₁ = 100 g, c₁ = 0.1 kcal/kg.°C=0.1 cal/g.°C, T₁ = 30°C

m₂ = 250 g, C₂=0.4 kcal/kg.°C = 0.4 cal/g.°C, T₂ = 30°C

m₃ = 10 g, T₃=0°C, L = 80 cal/g, T = ?

c _(water)=1 cal/g.°C

Q₁ (heat lost by calorimeter)=m₁ c₁ (T₁-T)
Q₂ (heat lost by liquid) = m₂c₂ (T₂-T)
Q₃ (heat absorbed by ice) = m₃L
Q₄ (heat absorbed by water formed on melting of ice) = m₃c (T- T₃) = m₃c (T-0°C)

T₁>T₃ , T₂>T_3,  T>T₃

According to the principle of heat exchange,

Q₁+Q₂=Q₃+Q₄

∴ m₁ c₁(T₁-T)+ m₂c₂(T₂-T)= m₃L + m₃c(T-0°C)

∴ m₁ c₁T₁ - m₁c₁T+ m₂c₂T₂- m₂c₂T= m₃L + m₃c (T-0°C)

∴ m₁ c₁T₁ + m₂c₂T₂ = m₃L + m₃c (T-0°C) + m₁c₁T + m₂c₂T

∴ m₁ c₁T₁ + m₂c₂T₂ = m₃L +(m₃c + m₁c₁ + m₂c₂)T

∴ 100 x 0.1 x 30 + 250 x 0.4 x 30 = 10 x 80 +(100 x 0.1+250 x 0.4+10 x 1) T

∴ (10 + 100 +10) T =(300 + 3000 - 800)°C

∴ 120 T = 2500°C

∴ T= 2500/120 °C =20.83°C

20.83°C is the temperature of the mixture.