SecondLawof
Thermodynamics
PC1431: Lecture 34
(Problem Set)
Note: Since we will not be able to conduct any group tutorial on the
Second Law, we will discuss these problems during our last lecture.
Please attempt them before the lecture. You may also look
PC1431 Lecture 32 - 33
Second Law of Thermodynamics:
Entropy
Entropy
So far we have seen some aspects of 2nd Law, but have not
made any general statement. More general statement can
be made in terms of entropy, introduced by Clausius in
1860s.
Entropy,
PC1431 Lectures 30 - 31
Second Law of Thermodynamics:
Heat Engines
Need for 2nd Law of Thermodynamics
Many processes (thermal or otherwise) satisfy the first law
(conservation of energy) but never occur, e.g,
Helium from a punctured balloon spread around
Extra Slides & Solutions
to Lectures 28 - 33
1 & 2 Laws of
Thermodynamics
st
nd
AdiabaticProcess
In an adiabatic process, there is
no heat transfer between the
system and its surroundings.
Minus sign missing
in original slide
The internal energy decreases
FirstLawof
Thermodynamics
PC1431 Lectures 28 - 29
Heat Q
System
Change in
Internal
energy U
Work W
Surroundings
ThermodynamicProcesses&
ThermodynamicProcesses&
Variables
Quasi-static process: Processes that are carried out slowly
enough so that the system
PC1431 Lecture 28
Kinetic Theory of
Gases
Molecular Model of an Ideal Gas
Assumptions
Large number of molecules; separation > dimension of
molecules. Molecules occupy negligible volume - treated as
point-like.
Obey Newtons laws of motion, but move rando
PC1431 Lectures 23 27
Oscillations,
Temperature & Heat,
Kinetic Theory of Gases
(Additional slides and solutions to
problems discussed in lectures)
Summary I : Describing SHM
A particle is said to perform simple harmonic oscillation if its
acceleration is
Oscillations:
Simple Harmonic Motion
Damped & Forced Oscillations
PC1431 Lectures 23 & 24
Examples of Oscillatory Motion
Mass on a spring
Pendulum (e.g., simple, physical, torsion)
Vibrations of a stringed musical instrument
Electromagnetic waves (light,
PC1431Lectures2122
AdditionalSlides&Solutionsto
Problems
Newtons Law of Gravitation
Newtons
&
Planetary Motion
Example: Halleys comet
Example:
Consider the motion of Halleys comet. The eccentricity of the
Consider
orbit is given by e = 0.967. The distance
PC1431Lectures2122
Newtons Law of Gravitation
Newtons
&
Planetary Motion
Newton, (apple) and Moon
Newton,
I deduced that the forces that keep the planets in their orbs must be
reciprocally as the squares of their distances from the centres about
which the
Angular
Momentum
Momentum
PC1431 Lecture 20
Vector (Cross) Product
Given two vectors A and B, the
vector product is another vector C.
The magnitude of C is:
It is equal to the area of
parallelogram formed by
the vectors.
The direction of C is
perpendicula
Rotational
Dynamics &
Rolling Motion
Rolling
PC1431 Lectures 18 19
Definition of Torque
Consider a force F acting on a rigid body at point P in the direction as
shown. The rod is pivoted so that it can only rotate about the point O.
F
Ftan = F sin
Then t
AdditionalSlides&
AdditionalSlides&
Solutionstoproblemson
Rotation
PC1431 Lectures 16 20
Puzzle:
Since is defined by:
How can the angular velocity be a vector if is not
a vector ?
Perhaps can be commutative for small angle?
How about infinitesimal rotatio
Rotationof
Rotationof
RigidBodies
PC1431 Lectures 16-17
Rigid Body Rotation
Rotation of an extended object - different parts of an object
have different linear velocities & accelerations.
Assumption that extended object is rigid (non-deformable,
internal
Linear Momentum, Collisions,
Centre of Mass, Rocket Propulsion
Centre
Extra slides & Solutions to Problems
discussed in Lectures 13 15
Momentum vs Kinetic Energy
Momentum
A
B
Consider two iceboats A and
B of mass m and 2m
respectively. Both are
stationary
Momentum, Collisions &
System of particles
System
PC1431 Lectures 13 15
Linear Momentum
Linear
Linear momentum tells us both something about the object and
something about its motion.
The linear momentum of a particle of mass m moving with velocity
v is d
Potential Energy
Potential
PC1431 Lectures 12 - 13
Potential Energy
Potential
Potential energy is energy associated with the position
(gravitational P.E.) or configuration (elastic P.E.) of an
object.
P.E. can be considered as stored energy that can be
co
Work, KE, PE &
Energy Conservation
Energy
Extra slides & Solutions to Problems
discussed in Lectures 10 12
Ex: Angle between vectors
Ex:
Find the angle between the two
vectors:
Motivation : Motion in vertical circle
Motivation
We have earlier analyzed the
Work & Kinetic Energy
Work
PC1431 Lecture 10
Scalar Product of 2 Vectors (Recall)
Scalar
The scalar product of any two
vectors A and B, denoted by
AB (read A dot B), is a
scalar quantity equal to the
product of the magnitude of the
two vectors and the cos
PC1431 Lecture 07
Newtons Laws of Motion
Philosophiae Naturalis Principia
Mathematica, Issac Newton, 1687
You may be able to find pdf
versions of the Principia in the
Internet, eg,
http:/www.archive.org/details/newtonspmathema00newtrich
Direct from Newton
PC1431: Lectures 4 - 6
Kinematics in 2 & 3 D:
Projectiles, Circular motion
& Relative Motion
Displacement in 2D & 3D Motion
As with 1D motion, the kinematic equations for 2D &
3D motion can be derived by using the vector
properties of displacement, veloci
PC1431: Lecture 03
Kinematics in
One Dimension
Kinematics
Describe motion in terms of space and time (Ignore the
agents that caused the motion).
Types of motion
Translational
Rotational
Vibrational
Particle approximation: We first assume that the movin
PC1431: Lecture 02
Tooling-Up: Measurements &
Simple Properties of Vectors
Quantities and Units
Experiments require measurements of physical
quantities.
Every measurement give a number (value depends on
units that goes with it.)
SI (metric) vs Imperial (B
Welcome
to
PC1431
(Extra slides)
Learning should be a joy and full of
excitement. It is lifes greatest adventure;
it is an illustrated excursion into the minds
of noble and learned men, not a
conducted tour through a jail.
Taylor Caldwell
We learn more by