Dimensional formula of specific heat capacity

There is a close relationship between heat and temperature for any state of matter, solid or liquid. Heat is a form of energy that a body can absorb or lose. Due to this phenomenon, the temperature of the body will change. For example, when you hold a steel spoon over the fire, it will absorb the heat energy, and therefore, the molecules will start to vibrate faster. This will cause an increase in its temperature. The exact opposite happens when the body starts to lose heat energy, decreasing its temperature. An attribute termed specific heat capacity is considered to understand the relationship between heat and temperature.

What is specific heat capacity, and how is it related to the temperature of a body?

According to thermodynamics, everybody will continue to exchange heat energy between a system and its surroundings to achieve thermal equilibrium. The concept of specific heat capacity and the formula of the potential difference comes into the role of play.

Thermal law of equilibrium

It’s better to understand thermal equilibrium before moving on to the details of specific heat capacity and the concept of the formula of potential difference. If two bodies are involved in heat transfer, then the amount of energy lost by one body will be absorbed by the other until both achieve thermal equilibrium, or the temperature of both the bodies will become equal.

For example, if body A is at 40°C and body B is at 70°C, heat will flow from the hotter body to the colder one. Therefore, the temperature of body B will decrease while that of body A will increase till both these bodies attain the same temperature.

Definition of specific heat capacity

The specific heat capacity is defined as the amount of heat energy absorbed per unit mass to raise the temperature by 1 degree. Similarly, the heat energy lost by the unit mass for lowering the temperature by 1 degree is termed as specific heat capacity. This can be further explained with the formula of potential energy examples.

The physical expression of specific heat capacity

The heat energy is directly proportional to its mass and temperature. For example, if the masses of two bodies are different, then the one with a higher mass will have more thermal energy than the other one. Similarly, if we consider two bodies at different temperatures, the body at a higher temperature will have more heat energy, which can be explained with the formula of potential energy examples.

Therefore, from this above explanation, we can consider that:

Q  ∝ mT

Where Q = heat energy

m = mass of the body considered

T = temperature of the body

This equation can be written as:

Q = cmT

Where c is termed as the specific heat capacity. It is a constant variable and won’t change for a particular material because its mass and temperature won’t change.

cmT = Q

c = Q/mT

This equation explains that the specific heat capacity is calculated as the amount of heat absorbed by the unit mass for changing its temperature by 1 degree.

Derivation of the dimensional formula of specific heat capacity

Dimensions help in understanding what attributes or units will impact a dependent unit and how. For example, if the dimensional formula has [M0], it means that mass won’t have any contribution to the attribute. Similarly, when the dimensions of two units are positive, they are directly proportional to each other. Therefore, if the value of a unit increases, it will have the same effect on the other value. When the units are related in terms of negative indices, it symbolises indirect proportionality.

From the above statement, the specific heat capacity is defined by the formula of potential differences like:

c = Q/mT

where c is the specific heat capacity

Q is the heat energy

m is the mass

T is the temperature of the body

Considering the independent units for dimensions, I,e, length (L), mass (M), and temperature (K), the dimensional formula of specific heat capacity and formula of potential energy meaning can be described as:

c =  [ML2T-2] / [M][K1]

Or, c =  [ML2T-2] / [M][K1][L0]

Or, c = [M1-1 . L2-0 . T-2 . K-1]

Or, c =  [M0L2T-2K-1]

Or, c = [L2T-2K-1]

So, the SI unit for specific heat capacity will be:

c = m2sec-2K-1

Or, c = JouleKg-1K-1

Conclusion

Specific heat capacity and formula of potential difference play a crucial role in determining thermal equilibrium, thermodynamics, enthalpy, and several other attributes. The behaviour of different objects on the application of heat energy depends on this particular attribute. For example, if a substance has a low specific heat capacity, it won’t require too much heat energy to change its temperature by 1 degree. As this particular physical attribute depends on several other units, the study of its dimensional formula helps determine its dependency and how it will change when the other factors are changed. Furthermore, the specific heat capacity plays a significant role in determining the maximum heat that it can absorb or lose before changing its states, thereby the formula of potential energy meaning.