P K Nag Exercise problems - Solved
Thermodynamics
Contents
Chapter-1: Introduction
Chapter-2: Temperature
Chapter-3: Work and Heat Transfer
Chapter-4: First Law of Thermodynamics
Chapter-5: First Law Applied to Flow Process
Chapter-6: Second Law of Thermodynamics
Chapter-7: Entropy
Chapter-8: Availability & Irreversibility
Chapter-9: Properties of Pure Substances
Chapter-10: Properties of Gases and Gas Mixture
Chapter-11: Thermodynamic Relations
Chapter-12: Vapour Power Cycles
Chapter-13: Gas Power Cycles
Chapter-14: Refrigeration Cycles
Solved by
Er. S K Mondal
IES Officer (Railway), GATE topper, NTPC ET-2003 batch, 12 years teaching
experienced, Author of Hydro Power Familiarization (NTPC Ltd)
, Benefits of solving Exercise (unsolved) problems of P K Nag
• The best ways is to study thermodynamics is through problems, you must
know how to apply theoretical concepts through problems and to do so you
must solve these problems
• It contains Expected Questions of IES, IAS, IFS and GATE examinations
• It will enable the candidates to understand thermodynamics properly
• It will clear all your doubts
• There will be no fear of thermodynamics after solving these problems
• Candidate will be in a comfortable position to appear for various competitive
examinations
• Thermodynamics- “the Backbone of Mechanical Engineering” therefore
Mastering Thermodynamics is most important many of the subjects which
come in later like Heat and Mass Transfer, Refrigeration and Air
Conditioning, Internal Combustion Engine will require fundamental
knowledge of Thermodynamics
Every effort has been made to see that there are no errors (typographical or otherwise) in the
material presented. However, it is still possible that there are a few errors (serious or
otherwise). I would be thankful to the readers if they are brought to my attention at the
following e-mail address:
S K Mondal
Page 2 of 265
, Introduction
By: S K Mondal Chapter 1
1. Introduction
Some Important Notes
Microscopic thermodynamics or statistical thermodynamics
Macroscopic thermodynamics or classical thermodynamics
A quasi-static process is also called a reversible process
Intensive and Extensive Properties
Intensive property: Whose value is independent of the size or extent i.e. mass of the system.
e.g., pressure p and temperature T.
Extensive property: Whose value depends on the size or extent i.e. mass of the system (upper
case letters as the symbols). e.g., Volume, Mass (V, M). If mass is increased, the value of
extensive property also increases. e.g., volume V, internal energy U, enthalpy H, entropy S, etc.
Specific property: It is a special case of an intensive property. It is the value of an extensive
property per unit mass of system. (Lower case letters as symbols) e.g: specific volume, density
(v, ρ).
Concept of Continuum
The concept of continuum is a kind of idealization of the continuous description of matter where
the properties of the matter are considered as continuous functions of space variables. Although
any matter is composed of several molecules, the concept of continuum assumes a continuous
distribution of mass within the matter or system with no empty space, instead of the actual
conglomeration of separate molecules.
Describing a fluid flow quantitatively makes it necessary to assume that flow variables
(pressure, velocity etc.) and fluid properties vary continuously from one point to another.
Mathematical descriptions of flow on this basis have proved to be reliable and treatment of fluid
medium as a continuum has firmly become established.
For example density at a point is normally defined as
⎛ m⎞
ρ = lim ⎜
+∀→0 +∀ ⎟
⎝ ⎠
Here +∀ is the volume of the fluid element and m is the mass
If +∀ is very large ρ is affected by the in-homogeneities in the fluid medium. Considering
another extreme if +∀ is very small, random movement of atoms (or molecules) would change
their number at different times. In the continuum approximation point density is defined at the
smallest magnitude of +∀ , before statistical fluctuations become significant. This is called
continuum limit and is denoted by +∀C .
⎛ m ⎞
ρ = lim ⎜ ⎟
+∀→+∀
⎝ +∀ ⎠
C
Page 3 of 265
, Introduction
By: S K Mondal Chapter 1
One of the factors considered important in determining the validity of continuum model is
molecular density. It is the distance between the molecules which is characterized by mean free
path (λ). It is calculated by finding statistical average distance the molecules travel between
two successive collisions. If the mean free path is very small as compared with some
characteristic length in the flow domain (i.e., the molecular density is very high) then the gas
can be treated as a continuous medium. If the mean free path is large in comparison to some
characteristic length, the gas cannot be considered continuous and it should be analyzed by the
molecular theory.
A dimensionless parameter known as Knudsen number, Kn = λ / L, where λ is the mean free
path and L is the characteristic length. It describes the degree of departure from continuum.
Usually when Kn> 0.01, the concept of continuum does not hold good.
In this, Kn is always less than 0.01 and it is usual to say that the fluid is a continuum.
Other factor which checks the validity of continuum is the elapsed time between collisions. The
time should be small enough so that the random statistical description of molecular activity
holds good.
In continuum approach, fluid properties such as density, viscosity, thermal conductivity,
temperature, etc. can be expressed as continuous functions of space and time.
The Scale of Pressure
Gauge Pressure
Vacuum Pressure
Absolute
Pressure
Local
atmospheric Absolute Pressure
Pressure
Absolute Zero
(complete vacuum)
At sea-level, the international standard atmosphere has been chosen as Patm = 101.325 kN/m2
Page 4 of 265
Thermodynamics
Contents
Chapter-1: Introduction
Chapter-2: Temperature
Chapter-3: Work and Heat Transfer
Chapter-4: First Law of Thermodynamics
Chapter-5: First Law Applied to Flow Process
Chapter-6: Second Law of Thermodynamics
Chapter-7: Entropy
Chapter-8: Availability & Irreversibility
Chapter-9: Properties of Pure Substances
Chapter-10: Properties of Gases and Gas Mixture
Chapter-11: Thermodynamic Relations
Chapter-12: Vapour Power Cycles
Chapter-13: Gas Power Cycles
Chapter-14: Refrigeration Cycles
Solved by
Er. S K Mondal
IES Officer (Railway), GATE topper, NTPC ET-2003 batch, 12 years teaching
experienced, Author of Hydro Power Familiarization (NTPC Ltd)
, Benefits of solving Exercise (unsolved) problems of P K Nag
• The best ways is to study thermodynamics is through problems, you must
know how to apply theoretical concepts through problems and to do so you
must solve these problems
• It contains Expected Questions of IES, IAS, IFS and GATE examinations
• It will enable the candidates to understand thermodynamics properly
• It will clear all your doubts
• There will be no fear of thermodynamics after solving these problems
• Candidate will be in a comfortable position to appear for various competitive
examinations
• Thermodynamics- “the Backbone of Mechanical Engineering” therefore
Mastering Thermodynamics is most important many of the subjects which
come in later like Heat and Mass Transfer, Refrigeration and Air
Conditioning, Internal Combustion Engine will require fundamental
knowledge of Thermodynamics
Every effort has been made to see that there are no errors (typographical or otherwise) in the
material presented. However, it is still possible that there are a few errors (serious or
otherwise). I would be thankful to the readers if they are brought to my attention at the
following e-mail address:
S K Mondal
Page 2 of 265
, Introduction
By: S K Mondal Chapter 1
1. Introduction
Some Important Notes
Microscopic thermodynamics or statistical thermodynamics
Macroscopic thermodynamics or classical thermodynamics
A quasi-static process is also called a reversible process
Intensive and Extensive Properties
Intensive property: Whose value is independent of the size or extent i.e. mass of the system.
e.g., pressure p and temperature T.
Extensive property: Whose value depends on the size or extent i.e. mass of the system (upper
case letters as the symbols). e.g., Volume, Mass (V, M). If mass is increased, the value of
extensive property also increases. e.g., volume V, internal energy U, enthalpy H, entropy S, etc.
Specific property: It is a special case of an intensive property. It is the value of an extensive
property per unit mass of system. (Lower case letters as symbols) e.g: specific volume, density
(v, ρ).
Concept of Continuum
The concept of continuum is a kind of idealization of the continuous description of matter where
the properties of the matter are considered as continuous functions of space variables. Although
any matter is composed of several molecules, the concept of continuum assumes a continuous
distribution of mass within the matter or system with no empty space, instead of the actual
conglomeration of separate molecules.
Describing a fluid flow quantitatively makes it necessary to assume that flow variables
(pressure, velocity etc.) and fluid properties vary continuously from one point to another.
Mathematical descriptions of flow on this basis have proved to be reliable and treatment of fluid
medium as a continuum has firmly become established.
For example density at a point is normally defined as
⎛ m⎞
ρ = lim ⎜
+∀→0 +∀ ⎟
⎝ ⎠
Here +∀ is the volume of the fluid element and m is the mass
If +∀ is very large ρ is affected by the in-homogeneities in the fluid medium. Considering
another extreme if +∀ is very small, random movement of atoms (or molecules) would change
their number at different times. In the continuum approximation point density is defined at the
smallest magnitude of +∀ , before statistical fluctuations become significant. This is called
continuum limit and is denoted by +∀C .
⎛ m ⎞
ρ = lim ⎜ ⎟
+∀→+∀
⎝ +∀ ⎠
C
Page 3 of 265
, Introduction
By: S K Mondal Chapter 1
One of the factors considered important in determining the validity of continuum model is
molecular density. It is the distance between the molecules which is characterized by mean free
path (λ). It is calculated by finding statistical average distance the molecules travel between
two successive collisions. If the mean free path is very small as compared with some
characteristic length in the flow domain (i.e., the molecular density is very high) then the gas
can be treated as a continuous medium. If the mean free path is large in comparison to some
characteristic length, the gas cannot be considered continuous and it should be analyzed by the
molecular theory.
A dimensionless parameter known as Knudsen number, Kn = λ / L, where λ is the mean free
path and L is the characteristic length. It describes the degree of departure from continuum.
Usually when Kn> 0.01, the concept of continuum does not hold good.
In this, Kn is always less than 0.01 and it is usual to say that the fluid is a continuum.
Other factor which checks the validity of continuum is the elapsed time between collisions. The
time should be small enough so that the random statistical description of molecular activity
holds good.
In continuum approach, fluid properties such as density, viscosity, thermal conductivity,
temperature, etc. can be expressed as continuous functions of space and time.
The Scale of Pressure
Gauge Pressure
Vacuum Pressure
Absolute
Pressure
Local
atmospheric Absolute Pressure
Pressure
Absolute Zero
(complete vacuum)
At sea-level, the international standard atmosphere has been chosen as Patm = 101.325 kN/m2
Page 4 of 265
