ICSE Class 10 Physics Chapter 11 Calorimetry

Chapter 11: Calorimetry

Syllabus

(i) Calorimetry: Meaning, Specific heat capacities, Principle of method of mixture, Numerical problems on specific heat capacity using heat loss and gain and the method of mixtures.

Scope of syllabus: Heat and its units (calorie, joule), temperature and its units (°C, K); Thermal (heat) capacity C'=Q/ΔT. (S.I. unit of C'), Specific heat capacity c = Q/m ΔT; (S.I. unit of c), Mutual relations between heat capacity and specific heat capacity, Values of c for some common substances (ice, water and copper). Principle of method of mixtures including mathematical statement. Natural phenomena involving specific heat; consequences of high sp. heat of water. Simple numerical problems.

(ii) Latent heat: loss and gain of heat involving change of state for fusion only.

Scope of syllabus: Change of phase (state); heating curve for water; latent heat; sp latent heat of fusion (S.I. unit). Simple numerical problems. Common physical phenomena involving latent heat of fusion.

A. Heat Capacity, Specific Heat Capacity and Its Measurement

11.1 Concept of Heat

We know that each substance is made up of molecules. The molecules in a substance are in a state of random motion and each molecule exerts a force of attraction on the other molecules. Thus molecules possess kinetic energy due to their random motion and potential energy due to the molecular attractive forces. The sum of the potential energy and kinetic energy is called their internal energy. The total internal energy of molecules of a substance is called its heat energy.

A hot body has more internal energy than an identical cold body. When a hot body is kept in contact with a cold body, the cold body warms up, while the hot body cools down. i.e., the internal energy of the cold body increases, while that of the hot body decreases. Thus there is a flow of internal energy from the hot body to the cold body when they are kept in contact. The energy which flows from the hot body to the cold body is called the heat energy or simply the heat. Thus

Heat is the internal energy of molecules constituting the body. It flows from a hot body to a cold body when they are kept in contact.

Like all other forms of energy, heat is also a measurable quantity. The measurement of the quantity of heat is called calorimetry.

Units of heat

Like other forms of energy, the S.I. unit of heat is joule (symbol J).

The other most commonly used unit of heat is calorie (symbol cal). It is defined as follows:

One calorie is the quantity of heat energy required to raise the temperature of 1 g of water through 1°C.

In the above definition, it has been assumed that the heat energy required to raise the temperature of 1 g of water through 1°C at each initial temperature is same. However this is not true due to non-uniform thermal expansion of water. Hence the precise definition of calorie (which is also called 15°C calorie) is given as follow:

One calorie is the heat energy required to raise the temperature of 1 g of water from 14-5°C to 15-5°C.

The unit calorie is related to the S.I. unit joule as follows:

1 calorie (or 1 cal) = 4-186 J or 4-2 J nearly*

Sometimes, calorie is a smaller unit of heat, so we use a bigger unit called the kilo-calorie (symbol kcal), where

1 kilo-calorie = 1000 calorie = 4200 J nearly.

One kilo-calorie is the heat energy required to raise the temperature of 1 kg of water from 14-5°C to 15-5°C.

The unit kilo-calorie is generally used for measuring the energy value of foods.

11.2 Concept of Temperature

On keeping a hot body in contact with a cold body, heat flows from the hot body to the cold body due to which the hot body gets cooled, while the cold body gets warmed.

The body which imparts heat is said to be at a higher temperature than the body which receives heat. Thus, temperature determines the direction of flow of heat.

When a body receives heat energy, the particles constituting the body start vibrating more vigorously and so its temperature rises provided its physical state or dimensions remain unchanged.

Thus temperature is defined as below.

Temperature is a parameter which tells the thermal state of a body (i.e., the degree of hotness or coldness of body). It determines the direction of flow of heat when two bodies at different temperatures are placed in contact.

If there is no transfer of heat between the two bodies placed in contact, they are said to be at same temperature, but it does not mean that they have equal amount of heat in them. In fact, temperature alone does not tell us the quantity of heat energy contained in a body. Experimentally, we find that by imparting the same quantity of heat energy to different bodies, they get heated to different temperatures. The amount of heat energy contained in a body depends on mass, temperature and the material of body.

Unit of temperature

The S.I. unit of temperature is kelvin (symbol K). The other most common unit of temperature is degree celsius (symbol °C). They are related as:

\[T \text{ K} = 273 + t \text{ °C}\]

or more precisely, T K = 273-15 + t °C

Thus by adding 273 (or 273-15) to the temperature in degree celsius, we get the temperature in kelvin. The zero of the kelvin scale (called absolute zero or 0 K) is the temperature at which the molecular motion ceases. It is equal to -273°C (or -273-15°C).

Thus a degree (or temperature difference) is same on both the celsius and kelvin scales i.e.,

\[\Delta t \text{ °C} = \Delta T \text{ K}\]

11.3 Factors Affecting the Quantity of Heat Absorbed to Increase the Temperature of a Body

The quantity of heat energy absorbed to increase the temperature of a body depends on three factors: (1) mass of the body, (2) the increase in temperature of the body, and (3) the material (or substance) of the body.

Experimentally it is observed that

(1) Objects with different mass made from the same substance absorb different amounts of heat energy to raise their temperature by the same amount. For example, to raise the temperature of 1 kg of water by 1°C, heat energy absorbed is 1 kcal, while to raise the temperature of 2 kg of water by 1°C is 2 kcal. Thus the amount of heat energy absorbed is directly proportional to the mass of the object i.e., \[Q \propto m\]

(2) Objects with equal mass made from the same substance absorb different amounts of heat energy to raise their temperature by different amounts. For example, to raise the temperature of 1 kg of water by 1°C, heat energy absorbed is 1 kcal, while to raise the temperature of same mass of water by 2°C is 2 kcal. Thus the amount of heat energy absorbed is directly proportional to the rise in temperature i.e., \[Q \propto \Delta t\]

(3) Objects of same mass but made from different substances absorb different amounts of heat energy to raise their temperature by the same amount. For example, if equal mass of water and copper are heated through 1°C, the amount of heat absorbed by water is nearly ten times the amount of heat absorbed by copper. Thus, the amount of heat energy absorbed depends on the substance of the object which is expressed in terms of its specific heat capacity c.

From the above observations (i) and (ii),

\[Q \propto m \text{ and } Q \propto \Delta t\]

or

\[Q = c m \Delta t\]

where c is the constant of proportionality which is called the specific heat capacity of the substance. It is the characteristic of the substance and is different for different substances.

11.4 Difference Between Heat and Temperature

11.5 Thermal (or Heat) Capacity (C' = Q/ΔT)

From our everyday experience we find that different bodies require different amounts of heat energy for equal rise in their temperature. This property of a body is expressed in terms of its thermal (or heat) capacity. The heat capacity of a body is defined as follows:

The heat capacity of a body is the amount of heat energy required to raise its temperature by 1°C (or 1 K).

It is denoted by the symbol C'. Thus,

Heat capacity C' = amount of heat energy supplied / rise in temperature

If on imparting an amount of heat Q to a body, its temperature rises through Δt °C (or ΔT K), then

Heat capacity of the body C' = Q / ΔT

* For calculations, we generally take 1 cal = 4-2 J

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