THERMODYNAMICS
Thermodynamics deals with quantitative relationship between heat and other forms
of energies.
Important terminology
System: part of the universe selected for the purpose of experimental or theoretical
investigation.
Surrounding: part of the universe other than the system.
Open system: exchanges mass as well as energy with the surroundings.
Closed system: exchanges only energy but NOT mass with surrounding.
Isolated system: exchanges neither mass nor energy with the surrounding.
Isothermal process: process carried out at a constant temperature.
Adiabatic process: process in which no heat energy enters or leaves the system.
Isobaric process: process carried out at constant pressure.
Isochoric process: process carried out at constant temperature.
Extensive properties: properties that depend on the amount of matter contained in
the system; eg :mass, volume,energy,heat capacity etc.
Intensive properties: properties that are independent of the amount of matter
contained in the system;eg: temperature, pressure, density, viscosity, specific heat
capacity .
State of a system:the conditions of existence of a particular system when it’s
macroscopic properties have definite values.
State variables: those macroscopic properties that characterizes the state of a system
eg : Temperature, pressure, volume and concentration as well as heat and work.
State functions: Thermodynamics parameters which depend only upon the initial and
final states of the system and are independent of how these changes are accomplished.
Eg: internal energy, enthalpy, entropy, free energy, pressure, temperature, volume etc.
Internal energy: it is the sum total of the energies stored in it by virtue of its
molecules. It is impossible to determine the exact value of internal energy hence we
take interest only in the difference in internal energy( E).
First law of thermodynamics (Helmholtz): for an isolated system, the sum of all the
forms of energies is constant at all times. q = E +w or E=q-w
For a cyclic process E1 =E2
At constant volume heat change is
that is q=w (work done = heat absorbed).
E=qv
At constant pressure heat change is
H=qp (
H= E=p v)
Enthalpy H is defined by the equation; H=E + PV. For process carried out at constant
pressure, the change in enthalpy is given by
H= E + p V. Enthalpy measures
the heat content at a constant pressure.
Relation between qr and qp: qr=
E =qp-p
V qr=qp-pV or qv=qp-n(RT)
n=(moles of product-moles of reactants.).R=8.314J/k mol.
Sign convention: Work done by the system(-ive);work done on the system(+ive).
Second law of thermodynamics:
1) heat cannot pass from a cooler to a hotter body.
2) Heat cannot be totally converted to mechanical work.
Entropy: State property, is a measure of the degree of disorder or randomness in a
given system. It measures the unavailable form of energy(TS). It accounts for the
irreversibility of the given change.
Spontaneous or natural process occurs under a given occurs under a given set of
conditions without being forced. They occur with increase in entropy and are
irreversible.
Mathematical expression for entropy: S=qrev/T,it is an extensive property and the
unit is J/K Mol.S=0 for a reversible process; S>0 for an irreversible
process.Entropy changes for an ideal gas:
S= 2.303n(Cv log T2/T1)+Rlog V2/V1) or S=2.303(Cp logT2/T1-RlogP2/P1)
Isothermal : ST = 2.303nRlogV2/V1=-2.303nRlogP2/P1
Isobaric process: SP=2.303nCplogT2/T1
Isochoric process : Sr=2.303nCrlog T2/T1
WORK:
Maximum work is done in a reversible
process.Wrev=2.303nRTlogV2/V1=2.303n/RTlogP1/P2
Work done in an irreversible process=Wirr=P2(V2-V1)101.3*10-3KJ.
Carnot cycle: calculates the maximum extent to which heat can be converted into
work.
1)A
B=W1=-2.303RT2logV2/V1
2)B
C=W2=-Cv(T2-T1)
(work done by the gas is –ive hence
-ive x –ive=+ive)
3)C
D=W3= 2.303RT1logV3/V4
4)D
A=W4= -E= -Cv(T2-T1)
Free energy and spontaneity of a chemical change
Free energy is a measure of a system’s ability to do work.The Gibbs free energy
or Gibbs function,G,is defined by G= H-TS
Where S=Entropy; H=Enthalpy; G=Energy liberated or absorbed in a reversible
process at constant pressure and constant temperature(T).Changes in Gibbs free
energy,G are useful in indicating the conditions under which a chemical reaction
would occur.G=0 for a system at equilibrium.
PositiveG value indicates that reaction will only occur if energy is supplied to force
it away from the equilibrium position.
Negative G value indicates that reaction will proceed spontaneously to equilibrium.
Physical significance of Gibbs free energy:Energy available for useful work.
q=E+Wexpansion +W non expansion ;q=heat absorbed;E=Change in internal energy.
Under constant pressure:q=E+PV+Wnon-expansion (work expansion=PV)
Q=H+Wnonexpansion (H=E+PV)Also S=q rev/Tqrev=TS
TS=H+Wnon expansion or H-TS=-Wnonexpansion also G=H-TS
-Wnonexpansion=G Example electrical work =-nFE.
Criterion for-ive value of G for spontaneity of a reaction:
Sign of H
Sign of S Sign of G
Negative
Positive
Negative
Spontaneous at all temperatures
Positive
Positive
Negative
Spontaneous at high tem[peratures.
Negative
Negative
Negative
Spontaneous at low temperatures.
Positive
Negative
Positive
Non spontaneous at all temperatures
Occurrence of reaction
CHEMICAL ENERGETICS
Q1).
a)The heat absorbed by a gas at 27C during isothermal reversible expansion is 3600
Joules. What is the entropy change of the gas.(1)
b) Ten moles of an ideal gas at 27C and 10 atm pressure occupying a volume of
234.6 litres undergoes the following transformations:
1) Isothermal and reversible expansion to 246l;
2) Isothermal and irreversible reaction to 246l.
3) Isochoric heating to 177C.
calculate the work done in each transformation and express it in KJ.(4).
c)State how entropy and free energy can be used as a criteria to determine the
spontaneity of a chemical change.(4)
Q2).
a). Under all circumstances the entropy change in a spontaneous proves is
positive.,(T/F).
b)1.When a system undergoes an isothermal change, how is the heat absorbed related
to the entropy change in the system?
2.Five moles of oxygen at 127C undergoes isothermal compression from 2atm to
10atm,.What is the entropy change of the system? The system, actually gave up
5.92Kcal of heat during the transformation. Is the transformation reversible or
irreversible?.(4)
c)A certain transformation at constant temperature can take place with the evolution
of 18Kcal of heat. The entropy change for the transformation at 300K is –15
cal/deg.Will this transformation be spontaneous at 300K?.(2)
Q3).
a) A spontaneous reaction is always accompanied by an increase in entropy(T/F)
b) 10dm3 of a gas at 300K and 100K pa pressure absorbs 100j of heat at constant
volume. What is the work done by the gas and the change in internal energy of the
gas.(2)
c)The standard free energy of formation in the gaseous state of methanol,dimethyl
ether and water are-38.7,27.3and-54.6Kcal respectively. Is the transformation of
methanol to dimethyl ether in the gaseous state spontaneous(1).
Q4).
a)Give the mathematical form of the first law of thermodynamics.(2)
b)2moles of an ideal gas expands isothermally and reversibly from 1L to 5L at 18C.
Calculate the work done.
c)What is the Carnot’s cycle?Derive the relationship between the net working and
heat changes involved in the Carnot’s cycle giving expressions for each of the
strokes.(7).