# Specific Heat Capacity Formula

## What is the Specific Heat Capacity Formula?

Specific heat is the heat energy required to change the temperature of one unit mass of a substance of a constant volume by 1 °C.

The specific heat capacity of a substance is the amount of energy needed to change the temperature by 1 unit of material of 1 kg mass.

The SI unit of specific heat and specific heat capacity is J/Kg. The specific heat formula, and the formula of specific heat capacity will be discussed here.

### Thermal Capacity Formula

The thermal capacity or heat capacity is a physical property of matter or substance. We define this property as the amount of heat supplied to a given mass of a material to generate a change of unit temperature.

The thermal capacity SI unit is Joule per Kelvin or J/Kg. Besides this, the heat capacity formula or the thermal capacity formula is:

C = lim $\frac{\Delta Q}{\Delta T}$

$\Delta$T → 0

Here,

Delta Q = It is the amount of heat that must be added to the object of mass  ‘M” to raise its temperature by delta T.

Also, the value of the above parameter varies considerably depending on the initial temperature {$\Delta$T} T of the object and the pressure {$\Delta$P}P applied to it.

### Molar Heat Capacity Formula

Molar heat capacity is the amount of heat needed for the temperature rise of a given substance by 1 ⁰C. The molar heat capacity formula is given by:

Cm = C/n

Here,

Cm = molar heat capacity

C = heat capacity

And,

n = number of moles

We see that “n” is the number of moles of the sample. The number of moles can be determined by the following formula:

= $\frac{\text{Quantity of a sample or mass of the substance}}{\text{molar mass}}$ = $\frac{m}{M}$

Now, let’s understand the specific heat capacity equation:

### Specific Heat Formula

The specific heat capacity formula is:

Q = mc$\Delta$t

Or,

c = $\frac{Q}{m\Delta t}$…....(1)

Here,

Q  is the heat energy

m = mass in Kg

c = specific heat capacity, and

$\Delta$t is the temperature change in Kelvin

Also, the change in temperature is given by:

Δ T = (Tf – Ti)

Where Tf is the final temperature and Ti is the initial temperature in K.

### Unit of Specific Heat Capacity

The unit of specific heat capacity is J/Kg. K, or J/Kg °C.

### Dimensional Formula of Specific Heat

The dimensional formula of specific heat is calculated as;

The dimensional formula of heat is [M$^{1}$ L$^{2}$T$^{-2}$]

The dimensional formula of m is [M$^{1}$L$^{0}$K$^{0}$]

The dimensional formula of  Δ T is [M$^{0}$L$^{0}$K$^{1}$]

Step 1: Now, putting the dimensional formulas of Q, m, and Δ T:

= $\frac{[M^{1}L^{2}T^{-2}]}{[M^{1}L^{0}K^{0}][M^{0}L^{0}K^{1}]}$

Step 2: Cancelling out the common terms:

=  [M$^{0}$L$^{2}$T$^{-2}$K$^{-1}$]

So, the dimensional formula of specific heat capacity is [M$^{0}$L$^{2}$T$^{-2}$K$^{-1}$].

### Specific Latent Heat Formula

Specific latent heat is the measure of the heat energy (Q) released/absorbed per mass (m) during a phase/state change.

The specific latent heat formula is:

Q = mL

Or,

L = $\frac{Q}{m}$

Here,

Q = the heat absorbed or released depending on the direction of the transition. It is    measured in  KJ

L = specific latent heat of the material. It is measured in KJ/kg.

m = mass of the substance. It is measured in Kg.

### Conclusion

The specific heat is the measure of heat per unit mass needed for the temperature rise by one degree Celsius. The connection between heat and temperature change is typically communicated in the structure that appeared underneath where c is specific heat.

Q1: Why is the Specific Heat Capacity Formula Used?

Ans: The specific heat formula is used to determine the specific heat of any given material, if any of the parameters, like mass, heat gained, or the difference in temperature is given. Its measuring unit is Joule/Kg Kelvin, abbreviated as J/Kg K.

The specific heat capacity formula helps us measure the specific heat capacity of a given material in Joule/Kilogram-Kelvin (abbreviated as J/Kg. K). The significance of specific heat capacity is: It is the amount of heat energy needed for the temperature rise of 1 kg of a substance by 1 K. Thus, it gives an important indication of how much energy will be needed to heat/cool the material of a given mass by a given amount.

Q2: What is the Specific Heat of Liquid?

Ans: At room temperature, the value of specific heat capacity (Cp) is roughly 4.2 J/g°C. This states that it takes 4.2 joules of energy to increase 1 gram of the temperature of water by 1 degree Celsius.

Q3: What is the Specific Heat of Milk?

Ans: According to the handbook "Dairy-Based Ingredients" of the American Association of Cereal Chemists, by Ramesh Chandan, skimmed milk has a specific heat of 3.97 J/g °C, and whole fat milk has a specific heat of 3.89 J/g °C. The cream of milk has a specific heat of 3.35 J/g °C.