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:

\[C = lim \frac{\Delta Q}{\Delta T}\]

\[\Delta T \rightarrow 0\]

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 {ΔT} T of the object and the pressure {ΔP}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:

C_m = C/n

Here,

C_m = 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:

\[= \frac{Quantity \, of \, a \, sample \, or \, mass \, of \, the \, substance}{molar \, mass} = \frac{m}{M}\]

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

\[\Delta \]

\[\Delta \]

t is the temperature change in Kelvin

Also, the change in temperature is given by:

Δ T = (T_f – T_i)

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 \[\Delta T\] is \[M^{0} L^{0} K^{1}\]

Step 1: Now, putting the dimensional formulas of Q, m, and \[\Delta T\]:

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

Step 2: Canceling 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.

Points to Remember

• Transferred heat depends on three factors which are - The change in temperature, the mass of the system, and the phase of a substance.

• The temperature change is directly proportional to the amount of heat transferred.

• Heat can be added twice to double the temperature and mass.

• Mass is directly proportional to the amount of heat transferred.

• Heat has to be added in order to cause an equivalent temperature change in a doubled mass.

• The amount of heat transferred depends on the materials and the phase.

• The specific heat power of water is 4.2 joules per gram per Celsius degree 

• The specific heat capacity of water is higher than than the metal

• The application of specific heat is used in the swimming pools.

• The constant volume of the specific heat capacity of steam is 1.4108 kJ/kg K.

• The constant pressure of the specific heat capacity of steam is 1.8723 kJ/kg K.

• The heat needed to raise a substance's temperature by 1 degree Celcius is called the specific heat capacity.

• The specific heat power of water is 4.2 joules per gram per Celsius degree.

• Q = C m ∆t is the formula for the specific heat capacity

Tips for Understanding the Topic

• Specific Heat capacity is an important chapter for competitive exams such as JEE Mains and BITSAT so this chapter is important in Physics.

• This chapter is also covered in the school so students are suggested to clear the concepts during the school which will help them for the further exams too.

• As this topic is important from an exams point of view the students are recommended to cover this topic.

• The students should understand the concept of specific heat capacity and can make notes regarding this topic.

• This chapter consists of the problems in which mathematical solutions are to be solved so students need to practice the problems so that they won't face problems during the exams.

• Make notes while the teacher teaches this will help them to make the running notes. This will make a brief understanding of this chapter.

• They can make their own personal notes by studying the chapters and referring to the external notes which are available on the website. This will make the students remember the topic and can refer for quick study.

• Practice the problems given in the textbooks, don't just stay with a single book for solving the questions. They should solve multiple questions from different books this will make the student more acquainted with a topic. 

• They can refer to the solution books for the solutions of the problems after they try to solve the question. By double-checking the steps used to answer the problem is correct or not and comparing the answer to that question will help the students to be sure if they can solve a problem or not. 

• Some students may face problems they should practice more that will make their concepts more clear.

• Clear the basic concepts of the topic so that it will be easy to understand and answer the questions.

• Students are recommended to have external guidance to prepare for the exam and they can guide them to study the right topic with better knowledge.

• If they get stuck in a problem or have any doubts they can ask the teachers or tutors so that they can help the students regarding the topic.

• Students should always revise the chapter after they finish studying. This will help the students to come up with doubts which they might have while revising the topic. Doubts help the student to know and gain more knowledge about the subject that might help them.

• Strengthen the math skills because this will help to solve the problems in Physics. 

• Students also have to remember the formula and have the knowledge of the formula to use it in the solution so that they can get the answers right.

• Students should learn the SI units for using the equations in the correct way. By this, it will be easy for them to simplify the equations and can get the answers they want.

Vedantu has everything prepared for the students so that students can have the materials that they need. Free notes and study materials of this are available on the website of Vedantu and can be downloaded with the help of a mobile or laptop. It can be downloaded in PDF form. Students can refer to the study material for their exams.

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.