1
CL260, Spring 2013
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 4
Date: 01/02/2012
1. For the canonical ensemble, obtain the derivatives ( E/V ),N and ( p/ )V,N to show that,
E
V
p
+
,N
= p
V ,N
On comparing with the thermodynamic equati

1
CL260, Spring 2014
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 2
Date: 26/01/2014
1. Given the Binomial expansion of (1 + x)M for x = O(1),
M
(1 + x)M =
M
tN
N =0
N =0
M !xN
,
N !(M N )!
show that the logarithm of the sum (LHS above) is

1
CL260, Spring 2014
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 5: Fluctuations
Date: 10/02/2014
1. Fluctuation theory shows that for the canonical partition,
(N, V, E )eE/kT ,
Q(N, V, T ) =
E
there is eectively only one term in this summ

1
CL260, Spring 2013
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 5: Fluctuations
Date: 12/02/2013
1. Fluctuation theory shows that for the canonical partition,
(N, V, E )eE/kT ,
Q(N, V, T ) =
E
there is eectively only one term in this summ

1
CL260, Spring 2012
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 4: Fluctuations
Date: 12/02/2012
1. Fluctuation theory shows that for the canonical partition,
(N, V, E )eE/kT ,
Q(N, V, T ) =
E
there is eectively only one term in this summ

Chapter 9
Forced Convection: Internal
Flows
(Material presented in this chapter are based on those in Chapter 8, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
In the previous chapter, estimation of heat and mass transport

CL242 Fundamentals of heat and mass transfer
Homework 2
Due 21/3/2011 (Monday) 5 PM
Instructions:
1. The questions for homework are from the problems section in chapters 2 to 5 in the book
Fundamentals of Heat and Mass Transfer, Fifth Edition by Frank P.

CL242 Fundamentals of heat and mass transfer
Homework 4
Due 12/4/2011 (Tuesday) 5 PM
Instructions:
1. The questions for homework are from the problems section in the book Fundamentals of
Heat and Mass Transfer, Fifth Edition by Frank P. Incropera and
Davi

Chapter 12
Heat exchangers
(Material presented in this chapter are based on those in Chapter 11, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
Heat exchanger is a device for heat exchange between two uids, say hot
and cold

Chapter 13
Interface mass transfer
(Material presented in this chapter are based on those in Chapters 8 and 13,
Diusion mass transfer in uid systems second edition by EL Cussler)
In chapter (7), methods to estimate mass transport coecients for transport
f

Chapter 15
Mass transfer with chemical
reactions
(Material presented in this chapter are based on those in Chapter 16, Diusion mass transfer in uid systems second edition by EL Cussler and Chapter
14, Fundamental of heat and mass transfer, second edition

Chapter 1
Conduction
(Material presented in this chapter are based on those in Chapters 2 & 3,
Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and
DeWitt)
1.1
Introduction to conduction
Transport of energy in a medium due to temperature

Chapter 8
Forced convection: External
ows
(Material presented in this chapter are based on those in Chapter 7, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
Forced convection occurs when the relative motion between the uid

Chapter 7
Introduction to Convection
(Material presented in this chapter are based on those in Chapters 6 and 7,
Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and
DeWitt)
Convective heat transfer is dened as the energy transfer betwee

Chapter 2
Conduction in extended
surfaces
(Material presented in this chapter are based on those in Chapter 3, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
2.1
Introduction
The systems that were considered had heat transf

Chapter 3
2-D Heat conduction
(Material presented in this chapter are based on those in Chapter 4, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
Consider a slab of width W and length L (Fig. 3.1). For sake of brevity,
assu

Chapter 10
Natural or free convection
(Material presented in this chapter are based on those in Chapter 9, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
In the previous two chapters, analytical expressions and correlations

1
CL260, Spring 2012
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 2
Date: 28/01/2012
1. For the binomial distribution,
(N1 ) =
N!
,
N1 !N2 !
it was shown that the the maximum in the above function occurs when N1 = N1 = N/2. Show that
)in t

1
CL260, Spring 2012
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 3
Date: 03/02/2012
1. For the canonical ensemble, obtain the derivatives ( E/V ),N and ( p/ )V,N to show that,
E
V
p
+
,N
= p
V ,N
On comparing with the thermodynamic equati

1
CL260, Spring 2012
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 5 & 6: Fluctuations & Ideal Monoatomic Gas
Date: 17/02/2012
1. In deriving the limiting case of Boltzmann statistics, we claimed that if the number of molecular
quantum state

1
CL260, Spring 2013
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 2(B)
Date: 23/01/2013
1. Consider an ensemble having 4 systems each which can be in any one of the four energy states:
E1 , E2 , E3 and E4 . The energy levels of the each ene

1
CL260, Spring 2013
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 3
Date: 01/02/2013
1. For the binomial distribution,
(N1 ) =
N!
,
N1 !N2 !
it was shown that the the maximum in the above function occurs when N1 = N1 = N/2. Show that
)2 in

1
CL260, Spring 2013
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 2
Date: 23/01/2013
1. Given the Binomial expansion of (1 + x)M for x = O(1),
M
(1 + x)M =
M
tN
N =0
N =0
M !xN
,
N !(M N )!
show that the logarithm of the sum (LHS above) is

1
CL260, Spring 2013
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 1
Date: 14/01/2013
1. Show that the energy eigenvalues of a free particle conned to a cube of length a are given by,
E=
h2
n2 + n2 + n2 , nx , ny , nz = 1, 2, .
y
z
8ma2 x
2.

1
CL260, Spring 2012
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 7: Diatomic Molecules
Date: 17/02/2012
1. The empirical Morse function for ue (r) is
ue (r) = De cfw_[1 ea(rre ) ]2 1
Find the force constant f in terms of De and a.
2
2. Fro

1
CL260, Spring 2014
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 1
Date: 26/01/2014
1. Show that the energy eigenvalues of a free particle conned to a cube of length a are given by,
E=
h2
n2 + n2 + n2 , nx , ny , nz = 1, 2, .
y
z
8ma2 x
2.

1
CL260, Spring 2014
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 4
Date: 03/02/2014
1. For the canonical ensemble, obtain the derivatives ( E/V ),N and ( p/ )V,N to show that,
E
V
p
+
,N
= p
V ,N
On comparing with the thermodynamic equati

1
CL260, Spring 2014
CL 260: Molecular and Statistical Thermodynamics
Tutorial - 4
Date: 01/02/2014
1. For the binomial distribution,
(N1 ) =
N!
,
N1 !N2 !
it was shown that the the maximum in the above function occurs when N1 = N1 = N/2. Show that
)2 in

Chapter 16
Simultaneous heat and mass
transport
(Material presented in this chapter are based on those in Chapters 20, Diffusion mass transfer in uid systems second edition by EL Cussler)
Processes that involve simultaneous heat and mass transfer are plen

Chapter 11
Boiling
(Material presented in this chapter are based on those in Chapter 10, Fundamentals of Heat and Mass Transfer, Fifth Edition by Incropera and DeWitt)
In this chapter, the process of heat transfer during phase change of a uid
will be char