Specific Heat vs. Heat Capacity

When we heat a substance, it starts absorbing heat up to a certain limit, after which, its temperature starts rising. This limit of a substance to tolerate or absorb heat without raising the temperature is termed heat capacity. Therefore heat capacity is defined as the amount of heat energy required to raise the temperature of a body by 1 °C or 1 °K.

Similarly, when the amount of body/substance is certain (1 kg), the amount of heat energy required to raise the temperature by 1 °C or 1 °K is termed specific heat capacity.

In both cases, the heat supplied is directly proportional to the absolute temperature change.

Heat change ∝ Absolute temperature change

q ∝ T

Heat capacity and specific heat capacity are two proportionality constants that relate to temperature change and the amount of heat.

Specific Heat Capacity vs Heat Capacity

Specific Heat Capacity Heat Capacity
Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by 1 °C or 1 °K
Heat capacity is the amount of heat required to raise the temperature of a substance by 1 °C or 1 °K
It is the amount of heat added or removed to change the temperature It is the ability of a body to absorb heat without increasing the temperature
It is not an intrinsic property It is an intrinsic property of a substance
Formula c= q/mT Formula C= q/T
The unit of specific heat capacity is J/g°C
The unit of heat capacity is J/°C
It is an intensive property so it depends on the amount of a substance It is an extensive property so it is independent of amount of a substance
Specific heat is specific for specific objects Heat capacity is a non-specific property

Examples of specific heat capacity are:

Water = 1 calorie or 4.182 J/g°C

Copper = 0.385 J/g°C

Examples of heat capacity are:

1 liter of water = 4182 J/kg°C

100 g of copper = 38.5 J/ °C

Heat Capacity

Heat capacity is the ability of the body to absorb heat. It is defined as the amount of heat energy required to raise the temperature of a substance by 1 °C.

Mathematical derivation:

When heat is absorbed by the body, its temperature changes. The temperature change is directly proportional to the amount of supplied heat.

q ∝ T

q = C.T

where,

  • C= heat capacity
  • q= heat absorbed by the body
  • T=change in temperature

C = q / T

The unit of heat capacity is J/°C. It is an intrinsic property of a substance since it is the potential of a substance to absorb heat.

Heat capacity is an extensive property. It depends on the mass or size of the object i.e. when the mass of an object increases, its heat capacity also increases. For example, 200g of Al requires twice the energy to change the temperature as required by 100g of Al.

Heat capacity is highly non-specific as it changes with the change in the amount of substance.

Related topics

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of 1 g of a substance by 1 °C.

Mathematical Derivation;

q ∝ m.T

q = m.c.T

where,

  • c = specific heat capacity
  • q = heat absorbed by the body
  • m = mass of a body
  • T = change in temperature

c = q / mT

The unit of specific heat capacity is J/g°C.

Specific heat capacity is an intensive property since it does not depend on the mass or size of the object i.e. when the mass of a substance increases, its specific heat capacity does not change. This capacity is highly specific to a substance.

The specific heat capacity of water is 4.18 J/g°C, which means that it takes 4.18 Joules of energy by 1 gram of water to increase its temperature by 1 °C. It does not matter, whether we have one drop or a sea full of water, its specific heat energy capacity will always be the same.

For example;

The heat capacity of water is 4.18 J/g°C and of iron is 0.45 J/g°C. It means that the change in temperature for water is smaller than iron upon similar heating because water has a high heat capacity since it absorbs a large amount of heat energy. Therefore, iron (Fe) heats or cools more quickly than water.

Another such example is on the beach when the sand has a greater temperature than the water in the sea, although both receive the same amount of energy from the sun. The reason again becomes the high specific heat capacity of water which leads to a temperature difference of up to 5 °C between beach sand and seawater.

Due to the large heat capacity of water, it has many applications, such as;

  1. Water is useful in storing thermal energy. For example, in nuclear reactors and geothermal plants, water plays the role of the middle man.
  2. The cooling system of automobiles uses water to carry away unwanted thermal energy.
  3. Living organisms have water as a major component in their cells which resists sudden temperature changes and maintains life.
  4. A central heating system such as hot water carries thermal energy through pipes from the boiler to the radiator. These radiators are fixed inside the house at suitable places which makes the ‘heating’ process occur.
  5. In solar cells, the heat energy absorbed from the sun is effectively stored by water, etc.

Key Takeaway(s)

Specific heat capacity vs heat capacity - specific-heat-vs-heat-capacity

Concepts Berg

What is the difference between thermal capacity and specific heat?

Thermal capacity means heat capacity or the ability of a body to absorb heat. Heat capacity is the amount of heat required to raise the temperature of a substance by 1°C. Its unit is J/°C. Specific heat capacity, on the other hand, is the amount of heat required to raise the temperature of 1 g of substance by 1°C. Its unit is J/g°C.

What is the relation between heat capacity and specific heat formula?

Heat capacity is the ratio of heat absorbed by the body to the change in temperature. It is represented by C. The formula of heat capacity is;

C = q / T

Specific heat capacity is the ratio of heat capacity to the mass of the body.  it is represented by c.

c = C / m

What is the difference between molar heat capacity and specific heat capacity?

Molar heat capacity is defined as the amount of heat required to raise the temperature of 1 mole of a substance by 1 °C. Its unit is J/mol0C.

Specific heat capacity is defined as the amount of heat required to raise the temperature of 1 gram of a substance by 1 °C. Its unit is J/g°C.

What is the specific heat capacity of air?

The specific heat capacity of air is 1000 J/kg.°K.

What is the specific heat capacity of water?

The specific heat capacity of water is 4.18 J/g°C.

What is the specific heat capacity of steam?

The specific heat capacity of steam is 1.99 J/g°C.

What are the applications of specific heat capacity?

Some applications of specific heat capacity are:

Substances having low heat capacity can be heated or cooled more rapidly. The substance with low heat capacity can show more changes in temperature more quickly. These substances are used in making heating pans, etc.

Similarly, water has a very high specific heat capacity which makes it usable in heating systems, heat transport systems, as a coolant, etc.

Is heat capacity the same as specific heat?

The heat capacity and specific heat are conceptually the same parameters with a small difference in mass dependence.

What is the specific heat of ice?

The specific heat capacity of ice is 2.09 J/g°C.

Why do different materials have different specific heat capacities?

Specific heat capacity is heat capacity per unit mass. As different materials have different masses (densities), they have different heat capacities too.

What are the temperature and specific heat relationships?

Temperature is a measure of the average kinetic energy of molecules whereas specific heat capacity is the energy required to raise the temperature of 1 gram of the substance by 1 °C.

The relation between temperature and specific heat capacity is;

c = Q / m.T

Hence, specific heat capacity is the amount of heat that is required to increase a certain temperature.

Is heat capacity a state function?

Heat capacity is not a state function as it does not depend on the initial and final state of the system. It is a path function and depends on the path taken by the system to bring a change.

What are the advantages of low specific heat capacity?

Low specific heat capacity means that less energy is required to increase the temperature. The materials having low specific heat capacity get warmed and cooled quickly as they cannot hold a greater amount of energy. Therefore these materials are used in making cooking utensils such as frying pans, kettles, etc for quicker food preparation.

Why does specific heat increase with temperature?

Specific heat is the amount of heat that a body absorbs. When the body absorbs energy in the form of heat, the collision between particles increases which increases the kinetic energy of the molecule. As the temperature is the measure of the average kinetic energy of molecules, temperature increases here as well.

Is heat capacity an extensive property?

Heat capacity depends on the size and mass of the object so it is an extensive property.

Why is CP greater than CV?

Cp is heat capacity at constant pressure and Cv is heat capacity at constant volume. When heat is supplied at a constant volume, no work is done because;

W = P V

W = 0

But when the heat is supplied at constant pressure then the substance expands and does work. Therefore, CP is greater than CV.

What are the units of specific heat?

The unit of specific heat capacity is J/g°C.

When does Cp become equal to Cv?

At absolute zero temperature (-273 °C or 0 °K), Cp becomes equal to Cv.

References

  • Heat Capacities: Liquids, Solutions, and Vapours edited by Emmerich Wilhelm (Institute of Physical Chemistry, University of Wein (Vienna), Austria), Trevor Letcher (Emeritus Professor, University of KwaZulu-Natal, Durban, South Africa)

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