The intensive property among the quantities below is

1. Thermodynamic terms:

(i) The system is the part of universe which is under thermodynamic consideration.

(ii) Everything in the universe that is not the part of the system is called surroundings.

(iii) Anything which separates the system from its surrounding is called boundary.

(iv) The property that depends on the mass or the size of the system is called an extensive property

(v) The property that is independent of the mass or the size of the system is called an intensive property.

(vi) A state function is a thermodynamic property of a system, which has a specific value for a given state and does not depend on the path (or manner) by which the particular state is reached.

(vii) A path function is a thermodynamic property of the system whose value depends on the path by which the system changes from its initial to final states.

2. Thermodynamic process

(i) Isothermal process is a thermodynamic process in which temperature of the system remain constant.

(ii) Adiabatic process is a thermodynamic process in which there is no exchange of heat energy between the system and its surrounding.

In adiabatic process, $\mathrm{P}{\mathrm{V}}^{\mathrm{\gamma }}=\text{constant or}\mathrm{ }{\mathrm{P}}_1{\mathrm{V}}_1^{\mathrm{\gamma }}={\mathrm{P}}_2{\mathrm{V}}_2^{\mathrm{\gamma }}$

(iii) Isochoric process is a thermodynamic process that takes place at constant volume.

(iv) Isobaric process is a thermodynamic process that takes place at constant pressure.

3. Internal energy:

(i) The total energy of all the molecules of the system is called internal energy.

(ii) The change in internal energy of a system is expressed as ΔU= Uf– Ui

4. Work:

Work is defined as the force (F) multiplied by the displacement(x). -w=F.x

5. Applications of thermodynamics:

(i) Mathematical form of the first law of thermodynamics is ΔU = q + w

(ii) The enthalpy (H), is a thermodynamic property of a system, is defined as the sum of the internal energy (U) of a system and the product of pressure and volume of the system.

$\mathrm{\Delta H} = \mathrm{\Delta U} + \mathrm{P\Delta V}$

$\mathrm{\Delta H} = \mathrm{\Delta U} +\mathrm{\Delta n}\left(\mathrm{g}\right) \mathrm{RT}$

(iii) The standard heat of formation of a compound is defined as “the change in enthalpy that takes place when one mole of a compound is formed from its elements, present in their standard states ($298 \mathrm{K}$and $1$  bar pressure)".

(iv) The heat of combustion of a substance is defined as “The change in enthalpy of a system when one mole of the substance is completely burnt in excess of air or oxygen”.

(v) Specific heat capacity of a system is defined as “The heat absorbed by one kilogram of a substance to raise its temperature by one Kelvin at a specified temperature”.

(vi) The heat capacity for $1$ mole of substance is called molar heat capacity.

6. Relation between ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$:

Relation between ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ for an ideal gas: ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\mathrm{nR}$

7. Enthalpy of reaction:

(i) The heat of solution is defined as the change in enthalpy when one mole of a substance is dissolved in a specified quantity of solvent at a given temperature.

(ii) The heat of neutralisation is defined as “The change in enthalpy when one gram equivalent of an acid is completely neutralised by one gram equivalent of a base or vice versa in dilute solution”.

(iii) The molar heat of fusion is defined as “the change in enthalpy when one mole of a solid substance is converted into the liquid state at its melting point”.

(iv) The molar heat of vaporisation is defined as “the change in enthalpy when one mole of liquid is converted into vapour state at its boiling point”.

(v) Molar heat of sublimation is defined as “the change in enthalpy when one mole of a solid is directly converted into the vapour state at its sublimation temperature”.

(vi) The heat of transition is defined as “The change in enthalpy when one mole of an element changes from one of its allotropic form to another.

8. Hess’s law :

(i) The enthalpy change of a reaction either at constant volume or constant pressure is the same whether it takes place in a single or multiple steps provided the initial and final states are same.

(ii) Lattice energy is defined as the amount of energy required to completely remove the constituent ions from its crystal lattice to an infinite distance from one mole of crystal.

9. Entropy and Spontaneity:

(i) Entropy is a measure of the molecular disorder (randomness) of a system.

$∆\mathrm{S}=\frac{{\mathrm{q}}_{\mathrm{rev}}}{\mathrm{T}}$

(ii) The second law of thermodynamics can be expressed in terms of entropy. i.e “the entropy of an isolated system increases during a spontaneous process”.

10. Gibbs Energy and Spontaneity:

(i) Gibbs free energy and the net work done by the system: -∆G=w-P∆V

(ii) The free energy change of the above reaction in any state is related to the standard free energy change of the reaction according to the following equation.

∆G=∆G°+RTln⁡Q

∆G°=-2.303RT log⁡K

11. The third law of thermodynamics

The third law of thermodynamics states that the entropy of pure crystalline substance at absolute zero is zero.

12. P-V diagrams:

(i) P-V diagram or indicator diagram is a graph showing the variation of pressure with the variation of the volume of a system.

(ii) Work done during isothermal process, w=nRT ln⁡V2V1=nRT ln⁡P1P2

(iii) Work done during adiabatic process, $\mathrm{w}=\frac{1}{\mathrm{\gamma }-1}\left({\mathrm{P}}_1{\mathrm{V}}_1-{\mathrm{P}}_2{\mathrm{V}}_2\right)=\frac{\mathrm{n}\mathrm{R}}{\mathrm{\gamma }-1}\left({\mathrm{T}}_1-{\mathrm{T}}_2\right)$

(iv) Slope of adiabatic curve is steeper than that of isothermal curve.

(v) Work done during isothermal expansion is more than the work done during adiabatic expansion if the initial and final volumes are same in both the cases.

(vi) Work done during isothermal compression is less than that during adiabatic compression if the initial and final volumes are same in both the cases.