Specific heats (Cv and Cp for monoatomic and diatomic gases)

Introduction

Specific heat is a principle that very few people discuss or are aware of when discussing the thermal characteristics of matter. The specific heat concept is used to determine how much heat is required to raise an object’s temperature by one degree in celsius and kelvin. Specific heat is described as the quantity of heat needed to increase the temperature of a substance. Alternatively, the specific heat is the amount of heat required to raise the substance’s temperature or substance under evaluation. In this article, we will look at specific heats (Cv and Cp for monatomic and diatomic gases), the formula for specific heat, a small derivation, and how to solve numerical problems.

What is specific heat?

Specific heat could be calculated as follows: When the two objectives, both at a different temperature, interact, heat always passes from warmer particles to colder particles until both reach an equal temperature. As per the Law of conservation of energy, the heat generated by initially colder particles must be equivalent to the heat lost by initially warmer material. 

The formula for specific heat is denoted by,

Q = C m ∆t

Here, 

• Q denoted the quantity of heat absorbed by a particle
• m denoted the mass of a body
• ∆t = Temperature (rise)
• C = Specific heat capacity of a particle.
• S.I unit of specific heat is J /kg.K

Cv and Cp represent specific heat at constant volume and constant pressure respectively.

What is the diatomic molecule?

A diatomic molecule, also known as a diatomic element, includes two chemically bonded atoms. Suppose the two atoms are similar, as in the oxygen molecule (O2). In that case, they form a homonuclear diatomic molecule, whereas if the atoms are different, as in the carbon monoxide particle, they establish a heteronuclear diatomic molecule (CO).

Additional rotational motions in diatomic molecules like polyatomic and oxygen molecules like liquid store heat energy in their kinetic energy of rotation. Because diatomic molecules could rotate about two axes, each additional degree of freedom adds more R to CV.

Some of the most common diatomic molecules are:-

• Hydrogen molecule (H2)
• Lithium molecule (Li2)
• An oxygen molecule (O2)
• Helium molecule (He2)

Occurrence

Hundreds of diatomic molecules have been recognised in the Earth’s environment, both in interstellar and labs. About 99 per cent of the Earth’s atmosphere is made up of 2 types of diatomic molecules: Nitrogen (78 per cent) and Oxygen (21 per cent). The natural presence of hydrogen in the Earth’s atmosphere is on the order of part per million. Furthermore, hydrogen is the most abundant diatomic molecule on the planet. Hydrogen atoms have the potential to dominate the interstellar medium.

What are monatomic elements?

A monatomic gas is a gas made up of particles and molecules made up of single atoms, such as helium or sodium vapour. They differ from diatomic, triatomic, or polyatomic gases in general. In the ordinary temperature range, a monatomic gas’s thermodynamic behaviour is extremely simple because it lacks the rotational and energy vibrational components that characterise polyatomic gases. As a result, its heat capacity depends on temperature, molecular or atomic weight, and entropy.

Some of the most common diatomic molecules are:-

• Argon
• Neon
• Radon
• Xenon
• Helium
• Krypton

Occurrence

Perfect gas, also referred to as an ideal gas, is a gas whose physical behaviour conforms to a specific idealised relationship between pressure, volume, and temperature, known as the general gas law. This Law, which we already know, is a generalisation that includes both Boyle’s Law and Charles’ Law as special cases and states what we already know for a given quantity of gas. In the equation PV = kT, T is the product of volume denoted by the letter V and pressure denoted by the letter P, and it is proportional to the absolute temperature T.

Conclusion

In the above notes, we have read about the Specific heats, monatomics and diatomics. Now, we can explain why water has a high specific heat by referring to hydrogen bonds. The molecules must vibrate to raise the temperature of the water due to the multitude of joined hydrogen bonds. Because there are so many hydrogen bonds, it takes more energy to break the water molecules by vibrating them. Similarly, it takes some time for hot water to cool down. Temperature drops as heat is dissipated, and water molecules’ vibrational movement slows. The heat emitted compensates for the cooling effect of heat loss from liquid water.