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. The measurement of the quantity of heat is called calorimetry. From our everyday experience, we find that different bodies require different amounts of heat energy for the equal rise in their temperature. This property of the body is expressed in terms of its thermal or heat capacity. The heat capacity of the body is the amount of heat energy required to raise the temperature by 1°C or 1 K, and is denoted by symbol C'. For example, if the heat capacity of a body is 60 JK-1, this means that 60 J heat energy is required to raise the temperature of that body by 1K or 1°C.
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Heat Capacity C' = Amount of heat energy supplied/rise in temperature If on imparting Q amount of heat to a body, its temperature rises through ∆t then C' = Q ∕ ∆t |
Units of heat capacity
The S.I unit of heat capacity is joule per kelvin or joule per degree C. The other common units of heat capacity are cal °C-1 and kcal °C-1.
1 kcal °C-1 = 1000 cal °C-1
1 cal K-1 = 4.2 J K-1
Heat capacity of the body when expressed in unit mass is called the specific heat capacity of the substance of that body. It is denoted by symbol c. The specific heat capacity is the characteristic property of the substance and is different for different bodies. The specific heat capacity of a substance is defined as the heat capacity per unit mass of a body of that substance.
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Specific heat capacity c = Heat capacity of the body C' / Mass of the body m as C' = Q ∕ ∆t Therefore, \(c = \frac{Q}{m \times \Delta t}\) or \(Q = c \times m \times \Delta t\) The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of unit mass of that substance through 1 °C or 1 K. |
The amount of heat energy absorbed to increase the temperature of a body depends on three factors:
Unit of specific heat capacity
The S.I unit of specific heat capacity is joule per kilogram per kelvin (J kg-1 K-1) or joule per kilogram per degree celsius (J kg-1 °C-1).
The other units of specific heat capacity are cal g-1 °C-1 and kcal kg-1 °C-1.
1 cal g-1 °C-1 = 4.2 × 103 J kg-1 K-1
For example, if the specific heat capacity of iron is .48 J∕g °C, this means that the heat energy required to raise the temperature of 1 g of iron by 1°C is 0.48 J.
| Heat Capacity | Specific Heat Capacity |
| It is the amount of heat energy required to raise the temperature of the entire body by 1°C. | It is the amount of heat energy required to raise the temperature of a unit mass of the body by 1°C. |
| It depends on the substance and the mass of the body; the more the mass more is its heat capacity. | It does not depend on the mass of the body; it is the characteristic property of the substance of the body. |
| Its unit JK-1 | Its unit J Kg-1K-1 |
Specific heat capacity is different for different substances. Usually, a good conductor has a low specific heat capacity while a bad conductor has a high specific heat capacity. If we heat the equal mass of two different substances on the same burner to give an equal amount of heat supply, we will notice that after the same time interval, the rise in temperature for two different substances is different. This is because of their different specific heat capacities. The substance with low specific heat capacity shows a rapid and high rise in temperature thus it is a better conductor of heat than the substance with high specific heat capacity which shows a slow and small rise in temperature.
Water has a high specific heat capacity (=4200 J Kg-1 K-1). The specific heat capacity is different for a substance in its different phases like for water, specific heat capacity is 4200 J Kg-1 K-1, of ice is 2100 J Kg-1 K-1 and steam is 460 J Kg-1 K-1.
| Substance | Specific Heat Capacity | |
| in J Kg-1 K-1 | in cal g-1 °C-1 | |
| Lead | 130 | 0.031 |
| Silver | 235 | 0.055 |
| Copper | 399 | 0.095 |
| Iron | 483 | 0.115 |
| Aluminum | 882 | 0.21 |
| Kerosene oil | 2100 | 0.50 |
| Ice | 2100 | 0.50 |
| Sea Water | 3900 | 0.95 |
| Water | 4180 | 1.0 |
Temperature and specific heat: The below graph shows how many degrees Celsius one gram of a specific material is raised by one calorie of heat.
Question 1: A metal piece of mass 50 g at 30 °C required 2400 J of heat energy in order to raise its temperature to 330 °C. Calculate the specific heat capacity of the metal.
Solution: Given, m = 50 g, heat energy = 2400 J, rise in temperature = 330 − 30 = 300 °C = 300 K.
Specific heat capacity \(c = \frac{2400}{50 \times 300} = .16 \) J g-1K-1
Question 2: What mass of a liquid A of specific heat capacity 0.84 J g-1 K-1 at a temperature 40 °C must be mixed with 100 g of a liquid B of specific heat capacity 2.1 J g-1 K-1 at 20 °C so that the final temperature of the mixture becomes 32 °C?
Solution: Fall in temperature of liquid A = 40−32 = 8 °C, Rise in temperature of liquid B = 32 − 20 = 12 °C
Heat energy is given by m gram of liquid A = m × 0.84 × 8 J
Heat energy taken by 100 gram of liquid B = 100 × 2.1 × 12 J
Assuming there is no heat loss, heat energy given by A = heat energy taken by B
m×0.84× 8 = 100×2.1×12 ⇒ m = 375 grams
