Specific Heat Formula

While discussing the thermal properties of materials, specific heat is a concept that very few people discuss and are aware of it. We use the specific heat concept to understand how much heat has to be supplied to raise the temperature of an object by a degree in kelvin or celsius. The amount of heat required to raise the temperature of the substance is known as the specific heat. In other words, the specific heat is the amount of heat required to change the temperature of the material or substance under consideration.

In this article, we will discuss what is specific heat, what is the formula of specific heat along with a small derivation, and solve numerical problems. 

Specific Heat Equation

We might have noticed in our day-to-day life if we consider heating or boiling water in two vessels of different volumes, the amount of heat required to boil the water at a certain time will completely depend on the volume of the water. In other words, if one vessel is containing more water than the other vessel, then the time taken by the vessel with more volume will be more than the other vessel. This implies that the amount of heat required to raise the temperature of any given substance is different and depends on the volume of the substance, this particular amount of heat required to vary the temperature is known as the specific heat or specific heat capacity.

We know that the term specific heat in thermodynamics refers to the ratio of the quantity of heat that we require to raise the temperature of a substance by one degree celsius that we need to increase the temperature of an equivalent mass of liquid (say water) by one-degree celsius. At the same time, we use the term specific heat for a more conventional reason to determine the amount of heat in calories that we require to raise the temperature of one gram of a material by one degree Celsius.

In simple words, the specific heat equation or the specific heat formula is the ratio of the amount of heat required to raise the temperature of a substance by one degree celsius to the amount of heat required to raise the temperature of the equal amount of water by one-degree Celsius at the room temperature.

The term specific heat is generally used when we are referring to something particular, such as we are referring to raising the temperature of a particular substance. Now, usually, everyone gets confused between the specific heat and the heat capacity. 

The heat capacity is the ratio of the quantity of heat required to alter the temperature by one degree Celsius, whereas the specific heat is the amount of heat required to raise the temperature of the substance, not just to change or alter the temperature of the material. One important point to note down here is that when we consider a particular amount of mass we tend to use the word Specific Heat or Specific Heat Capacity. The specific heat capacity of most of the thermodynamic systems is not constant and it depends on physical entities such as pressure, volume, and temperature.

Derivation

Now, let us have a look at the specific heat formula, which is denoted by the letter C. According to the definition of the specific heat, we have seen that it is directly proportional to the temperature change (in particular raising temperature). We know that amount of heat required (Q) is directly proportional to the change in temperature, thus we write:

⇒ Q ∝ ΔT ……(1)

Where,

ΔT is the change or raise in the temperature

Also, we know that the specific heat is also directly proportional to the mass of the substance under consideration, thus we get:

⇒ Q ∝ m ……..(2)

Where,

m is the mass of the substance

Combining equations (1) and (2) we get:

⇒ Q ∝ mΔT

⇒ Q = CmΔT

Where,

C is the specific heat 

Thus, the specific heat equation is given by:

C =  \[\frac{Q}{m \Delta t}\]

or

C = \[\frac{\Delta Q}{m \Delta t}\] joules/kg \[^{0}\]c ……..(3)

Where,

ΔQ is the amount of heat gained or lost in joules

ΔT is the change or raise in the temperature in degree celsius

m is the mass of the substance in kg 

Equation (3) is known as the specific heat equation or specific heat formula in physics and it is used to solve specific heat examples and to estimate specific heat of substance in real life. The specific heat substance will vary depending on the type of substance.

Specific Heat Examples

Now, let us have a look at a few specific heat examples that will help us to understand the concept of specific heat and the specific heat equation or the specific heat formula in a better way. 

1) If 968 joules of heat is required to raise the temperature of the 50 g of substance from 3000c to 4000c. Then, calculate the specific heat of the substance.

Solution:

Given, amount of heat required = Q = 960 joules

The mass of the substance = m = 50 g

The change in temperature = ΔT = T₂ - T₁ = 40 - 30 = 100C 

Now, we are asked to determine the specific heat of the substance. We know that the specific heat or the specific heat capacity is given by the equation:

⇒  C = \[\frac{Q}{m \Delta T}\]

Where,

Q - The amount of heat required

ΔT - The change or raise in the temperature

m - The mass of the substance

Substituting the required values in the above equation we get:

⇒ C = \[\frac{Q}{m \Delta T}\] = \[\frac{968}{50 \times 10}\]

 = 96850×10

⇒ C = 1.936 joules/g 0c

Therefore, the specific heat capacity of the substance is 1.94 joules/g 0c.

2) Calculate the heat required to raise 6kg of water from 400 C to 800 C? (Specific heat of water = 4.2 X 10³ J/kg 0c)

Solution:

Given, the mass of the water = m = 6kg

The change in temperature = ΔT = T₂ - T₁ = 80 - 40 = 400c  

The specific heat capacity of the water = C = 4.2 x 10³J/kg0c 

Now, our aim is to determine the amount of heat required to raise the temperature of 6kg of water from 4000c to 8000c. Thus, we know that the amount required is given by the equation:

⇒ Q = CmΔT

Where,

C - The specific heat of the substance

ΔT - The change or raise in the temperature

m - The mass of the substance

Substituting, required values in the above expression:

⇒ Q = CmΔT = (4.2 x 10³) (6) (40)

⇒ Q = 10.08 x 10⁵ J

⇒ Q = 1008 kJ

Therefore, the amount of heat required to raise 6kg of water from 4000c to 8000c is 1008 kJ.