Unit Thermodynamics is meant for the students of Class XII students of preferably CBSE syllabus

1. By
ARUNESH GUPTA
PGT (Chemistry) KV Barrackpore (AFS)
THERMODYNAMICS

2. A homogeneous thermodynamic system is defined as the one
whose chemical composition and physical properties are the same in
all parts of the system, or change continuously from one point to
another. ... The homogeneous bodies of a heterogeneous system are
referred to as phases.
• Topics to discuss
• System & surrounding & universe.
• System
(a) Open system
(b) Closed system
(c) Isolated system
(d) Homogeneous system &
(e) heterogeneous system

3. E.g. Work, heat etc.
State functions: n, P, V, T, U, H, S. G, etc
( depends on the state of system, value depends
on the initial & final state of system.
Path function: depends on the path by which the
change in the system is brought about.

4. Extensive & intensive properties:
Extensive properties: →depends upon the amount of
substance in the system.
e.g. mass, volume, energy, heat capacity, enthalpy, entropy ,
Gibbs’s energy etc
Intensive properties: →do not depend upon the amount of
substance in the system, depends upon the nature of the
substance e.g. temperature, pressure, refractive index, density ,
m.p., b.p., surface tension etc.
The ratio of two extensive properties is intensive property.
E.g. (i) density = mass / volume (ii) molar heat capacity Cm = C/n
etc.

5. Thermodynamic processes
(a) Isochoric system
(b) Isobaric system
(c) Isothermal system
(d) Adiabatic system

6. (a) Isochoric system:
Volume constant, ∆V = 0 , Closed system
(b) Isobaric system,
Pressure constant, ∆P = 0 , Open system
P
V
Work done = ?
Work done is the area covered by the line or curve in P-Vgraph
(a)
P
V
(b)

7. p
V
T constant
P
V
T constant
Here q, P, V change, Conducting
wall, also called diathermic
process

8. Cyclic process is a process in which a system returns to the original state
after a number of successive changes.
The change in the value of a property (X) which is a state function in a cyclic
process is zero. ∆U = 0 & ∆H = 0
Graphical representation of cyclic process:

9. Different types of graphs:

11. Internal energy (∆U) & enthalpy change (∆H):
∆U = qV = heat change at constant volume (Isochoric process)
Enthalpy (H) = U + PV
At constant T & P, ∆H =∆U +P∆V and ∆H = qP
Also, For a gareous reactions of ideal gases, P∆V = ∆n(g) RT
Hence, ∆H = ∆U + P∆V = ∆n(g) RT & qP = qV + ∆n(g) RT
In a bomb calorimeter, volume is constant so we calculate ∆U = qV
In an open vessel, P is constant, so we can calculate ∆H = qP
For reactions involving solids & liquids ∆n(g) = 0 ∆H = ∆U & qP = qV
For gaseous reactions;
(a) If ∆If ∆n(g) = 0 or ∆n(r} = ∆n(p} so, ∆H = ∆U & qP = qV :eg H2 (g) + I2g) → 2HI(g)
(b) If ∆n(g) >0 or ∆n(r} > ∆n(p} so, ∆H > ∆U & qP >qV : eg PCl5 (g) → PCl3(g) +Cl2(g)
(c) If ∆n(g) < 0 or ∆n(r} < ∆n(p} so, ∆H < ∆U & qP <qV :eg N2(g) + 3H2(g) → 2NH3(g)

12. Heat capacity (C) of a substance is defined as the amountbof heat
required to raise the temperature of a substance through 1ºC.
C = q/∆T or q = C∆T
Specific Heat Capacity (c) is the amount of heat required to raise the
temperature of 1g of a substance through 1ºC.
c = q / m∆T or, q = mc ∆T
Molar heat capacity (Cm) is the amount of heat required to raise the
temperature of 1mole of a substance through 1ºC.
Cm = C/n = q / n∆T 0r, q = Cm.n.∆T
Heat capacity of an ideal gas at constant volume Cv = [dU/dT]v
Heat capacity of an ideal gas at constant pressure CP = [dH/dT]P

13. For one mole of an ideal gas: Cp -Cv = R
For n mole of an ideal gas: Cp - Cv = nR
Cp/Cv = γ
γ decreases with the increase in temperature
Nature of gas monoatomic
eg, He, Ne etc
Diatomic
O2, N2 etc
Triatomic
SO2, CO2 etc
Cp/Cv = γ 1.66 1.40 1.30

14. To prove: Cp/Cv = γ 1.66 for a monoatonic gas.
For1 mole of a monoatomic gas, the internal energy (U)
U = (3/2) RT or, & Cp - Cv = RR
dT
dU
Cv
2
3
)( 
Hence, Cp - 3/2 R = R or, Cp = 5/2 R
Therefore,
66.1
3
5
2
3
2
5

R
R
C
C
v
P

15. Thermodynamic equilibrium:
(a) Thermal equilibrium: → no flow of heat from one part to another,
i.e. T = constant
(b) Mechanical equilibrium: no flow of matter from one part to
another. i.e. P= constant
(c) Chemical equilibrium: no change in composition of any part of the
system with time. [conc.] = constant.

16. WORK AND HEAT
Work is a form of energy transferred between system and surrounding.
Work is done by the system on the surrounding when heat is
transferred from system to surrounding. Expansion work.
Here Vinitial < Vfinal i.e. Wexpansion < 0 or -ve wexp = -Pext∆V.
Work is done on the system when heat is transferred from
surrounding to system. Compression work.
Here Vinitial > Vfinal i.e. wcompression > 0 or +ve wconp.= +Pext∆V
(a) Mechanical Work:(expansion work) Work of expansion or
compression or pressure-volume work. Mechanical work = Force x
Displacement.
(b) Electrical Work:(non expansion work) The force is the
electromotive force (emf) of the cell & quantity of electricity displaced.
Welect.= - (emf).(quantity of charge of electricity).

17. First law of thermodynamics:
(1) Energy can not be created or destroyed but can be
converted from one form to other. The total energy of universe
is constant.
(2) It is impossible to construct a perpetual motion machine.
(3) There is an exact equivalence between heat and work
( 1cal = 4.184 J)
Mathematically: ∆U = q + w = q - P∆V (as wexpansion = -Pext.∆V
q & w are not state function but q + w = ∆U is a state function.
∆U of an ideal gas depends only on temperature.
For isothermal process of an ideal gas ∆U = 0, so q =-w.
For irreversible isothermal process: q = -wirrev = P∆V = P(Vf - Vi)
For reversible isothermal process:
q = -wrev = nRT ln Vf /Vi = nRT lnPi/Pf,
For isothermal expansion of an ideal gas in vacuum (at constant T}
Pext = 0, w = 0, ∆U = 0 hence ∆ H = 0
For adiabatic change q=0 so, ∆U = wadia

18. Remember:

21. Adiabatic Processes for an Ideal Gas
An adiabatic process is one in which no energy is transferred by
heat between a system and its surroundings.
q = 0
For example, if a gas is compressed (or expanded) very rapidly,
very little energy is transferred out of (or into) the system by heat,
and so the process is nearly adiabatic.
Here the temperature of a system changes in an adiabatic process
even though no energy is transferred by heat.
In general, an adiabatic process is one in which no energy is
exchanged by heat between a system and its surroundings.

22. Let us suppose that an ideal gas undergoes an adiabatic expansion.
At any time during the process, we assume that the gas is in an
equilibrium state, PV = nRT so that the equation of state is valid.
The pressure and volume at any time during an adiabatic process are
related by the expression.
PVʏ = constant
where γ = CP / CV is assumed to be constant during the process.
Thus, we see that all three variables in the ideal gas law - P, V, and T -
change during an adiabatic process.
Adiabatic process for an ideal gas

23. Proof ; PVγ = constant for an Adiabatic Process
Let us take the infinitesimal change in volume to be dV and the
infinitesimal change in temperature to be dT at q = 0 between
system & surrounding.
The work done by the gas is P dV.
Because the internal energy of an ideal gas depends only on
temperature, the change in the internal energy in an adiabatic
expansion is the same as that for an isovolumetric process between
the same temperatures,
dUint = nCV dT
Hence, the first law of thermodynamics, ΔUint = Q – W, with Q = 0
becomes
ΔUint = – W,
dUint =nCvdT =-PdV
For ideal gas PV = nRT, PdV + VdP = nR dT
Eliminating dT,
PdV +VdP = -(R PdV)/CV

24. Substituting CP - CV = R (for i mole of an ideal gas)
Integrating, ln P + γ lnV = constant
PVγ = constant
PiVi
γ = PfVf
γ
Also, TVγ-1= constant, so, TiVi
(γ-1) = TfVf
(γ-1)
Also, TγP(1-γ) = constant, so, Ti
γPi
(γ-1) = Tf
γPf
(γ-1)

25. Thermochemical Equations:
Standard states: 298 K & 1 bar pressure & 1M solution＃
(1) Standard enthalpy of reaction ( ∆rHƟ )
(2) Standard enthalpy of combustion ( ∆cHƟ )
(3) Calorific value of foods & fuels
(4) Standard enthalpy of formation ( ∆fHƟ )
For a chemical reaction
Standard enthalpy of reaction ( ∆rHƟ ) = ∑( ∆fHƟ )(Products)-∑( ∆fHƟ )(Reactants)
Standard enthalpy of neutralisation( ∆neutHƟ )
H+(aq) + OH- (aq) → H2O (l) ∆neutHƟ = -57.1 kJ /mol (strong acid+strong base)
= -13.7 kcla/equivalent
Dissociation enthalpy of weak acid or base = ( ∆HƟ ) (H+ + OH-) - ( ∆neutHƟ )(released)

26. Standard enthalpy of solution ( ∆solHƟ )
∆solHƟ
= ∆latticeHƟ - ∆hydHƟ
Born Haber Cycle & ∆latticeHƟ
Standard enthalpy of atomization, ∆aHƟ
Standard enthaly of ionization; ∆lHƟ

27. The Adiabatic Process of an Ideal Gas
It is unusual to develop the equations of the Adiabatic Process directly from
the energy equations, since they are usually introduced after the discussion of
entropy as the Isentropic Process. This approach was introduced to us by
Potter and Somerton in their Schaum's Outline of Thermodynamics for
Engineers, and enables early meaningful analysis of the adiabatic processes in
Diesel and Otto cycle engines.
Consider a stationary closed adiabatic system in which the only energy
interaction is boundary work, that is, all other work and heat interactions are
excluded. The differential form of the energy is thus: