Take some water in a vessel and start heating it on a burner. Soon you will notice that bubbles begin to move upward. As the temperature is raised the motion of water particles increases till it becomes turbulent as water starts boiling.
What are the factors on which the quantity of heat required to raise the temperature of a substance depend? In order to answer this
question in the first step, heat a given quantity of water to raise its temperature by, say 20 °C and note the time taken.
Again take the same amount of water and raise its temperature by 40 °C using the same source of heat.
`"Note"` the time taken by using a stopwatch. You will find it takes about twice the time and therefore, double the quantity of heat required raising twice the temperature of same amount of water.
In the second step, now suppose you take double the amount of water and heat it, using the same heating arrangement, to raise the
temperature by 20 °C, you will find the time taken is again twice that required in the first step.
In the third step, in place of water, now heat the same quantity of some oil, say mustard oil, and raise the temperature again by 20 °C. Now note the time by the same stopwatch. You will find the time taken will be shorter and therefore, the quantity of heat required would be less than that required by the same amount of water for the same rise in temperature.
The above observations show that the quantity of heat required to warm a given substance depends on its mass, m, the change in
temperature, ΔT and the nature of substance.
The change in temperature of a substance, when a given quantity of heat is absorbed or rejected by it, is characterised by a quantity called the heat capacity of that substance. We define heat capacity, S of a substance
`S = (DeltaQ)/(DeltaT)`.....(11.10)
where ΔQ is the amount of heat supplied to the substance to change its temperature from `T` to `T + ΔT.`
You have observed that if equal amount of heat is added to equal masses of different substances, the resulting temperature changes
will not be the same.
It implies that every substance has a unique value for the amount of heat absorbed or rejected to change the
temperature of unit mass of it by one unit. This quantity is referred to as the `"specific heat capacity"` of the substance
If ΔQ stands for the amount of heat absorbed or rejected by a substance of mass m when it undergoes a temperature change ΔT, then the specific heat capacity, of that substance is given by
`s =S/M = 1/m (ΔQ)/(ΔT)`......(11.11)
The specific heat capacity is the property of the substance which determines the change in the temperature of the substance (undergoing no phase change) when a given quantity of heat is absorbed (or rejected) by it. It is defined as the amount of heat per unit mass absorbed or rejected by the substance to change its temperature by one unit.
It depends on the nature of the substance and its temperature. The SI unit of specific heat capacity is `J kg^(–1) K^(–1).`
If the amount of substance is specified in terms of moles μ, instead of mass m in kg, we can define heat capacity per mole of the
`C = S/mu = 1/mu (ΔQ)/(ΔT)`......(11.12)
where C is known as molar specific heat capacity of the substance.
Like S, C also depends on the nature of the substance and its temperature.
The SI unit of molar specific heat capacity is `J mol^(–1) K^(–1).`
However, in connection with specific heat capacity of gases, additional conditions may be needed to define C. In this case, heat transfer
can be achieved by keeping either pressure or volume constant.
If the gas is held under constant pressure during the heat transfer, then it is called the molar specific heat capacity at constant pressure and is denoted by `C_p.`
On the other hand, if the volume of the gas is maintained during the heat transfer, then the corresponding molar specific heat capacity is called molar specific heat capacity at constant volume and is denoted by `C_v`.
Table 11.3 lists measured specific heat capacity of some substances at atmospheric pressure and ordinary temperature while Table
11.4 lists molar specific heat capacities of some gases.
From Table 11.3 you can note that water has the highest specific heat capacity compared to other substances. For this reason water is
used as a coolant in automobile radiators as well as a heater in hot water bags.
Owing to its high specific heat capacity, the water warms up much more slowly than the land during summer and consequently wind from the sea has a cooling effect. Now, you can tell why in desert areas, the earth surface warms up quickly during the day and cools quickly at night.
A system is said to be isolated if no exchange or transfer of heat occurs between the system and its surroundings. When different parts of an isolated system are at different temperature, a quantity of heat transfers from the part at higher temperature to the part at lower temperature.
The heat lost by the part at higher temperature is equal to the heat gained by the part at lower temperature. Calorimetry means measurement of heat.
When a body at higher temperature is brought in contact with another body at lower temperature, the heat lost by the hot body is equal to the heat gained by the colder body, provided no heat is allowed to escape to the surroundings. A device in which heat measurement can be made is called a `"calorimeter."`
It consists a metallic vessel and stirrer of the same material like copper or alumiunium. The vessel is kept inside a wooden jacket which contains heat insulating materials like glass wool etc.
The outer jacket acts as a heat shield and reduces the heat loss from the inner vessel. There is an opening in the outer jacket through which a mercury thermometer can be inserted into the calorimeter.
The following example provides a method by which the specific heat capacity of a given solid can be determinated by using the principle, heat gained is equal to the heat lost.