CHAPTER 17: Temperature, Thermal Expansion, and the Ideal Gas Law
Responses to Questions
2.
Properties of materials that could be exploited in making a thermometer include:
a.
thermal expansion, both
PHYSICS 4B
FINAL EXAM
SPRING QUARTER 2013
PROF. HIRSCH
8 Problems
JUNE 11th
Please write in pen rather than in pencil. No regrading for finals written in pencil.
Write clearly and justify all steps.
P
Question
Viscous liquid of constant density and constant kinematic viscosity is at
rest in the region o y h between two rigid parallel plates. There are
no body forces. At time t = 0 the top plate is
Question
(i) Using tensorial notation, or otherwise, prove the vector identities
.(a) = .a + (a.)
( a) = 2 a + (.a)
a ( a) = (a2 /2) (a.)a
for a general suitably differentiable scalar function and ve
Question
Steady viscous incompessible flow takes place parallel to the z-axis in a cylindrical pip of cross section D. The kinematic viscosity and density of the fluid
are both constant and are given
H.P. Paar
PHYS 4B: Mechanics, Fluids, Waves & Heat
Spring 2015
Quizz # 3 solutions
Solutions by Yury Kiselev
1. (15 points)
(a) (5 points) Distance from the station L = vT tt = vL tL .
The problem cou
H.P. Paar
PHYS 4B: Mechanics, Fluids, Waves & Heat
Spring 2015
Quizz # 1 solutions
Solutions by Yury Kiselev
1. (25 points)
(a) (10 points) Lets set y = 0 at a position of the mass along vertical axis
Question
Define the Reynolds number Re for a viscous flow. YOU MAY ASSUME
that a suitable non-dimensional form of the steady Navier-Stokes equations
for use in studying boundary layer theory is
(q.)q
H.P. Paar
PHYS 4B: Mechanics, Fluids, Waves & Heat
Spring 2015
Quizz # 2 solutions
Solutions by Yury Kiselev
1. (15 points) Density of the water is higher than density of the ice, so a given volume of
PHYSICS 4B
PROF. HIRSCH
QUIZ 4
3 Problems
SPRING QUARTER 2014
May 19th
Problem 1 (10 pts)
An ideal gas has 32,000 molecules moving with velocity in the x direction in the range
-1m/s to 1m/s, and 16,0
CHAPTER 18: Kinetic Theory of Gases
Responses to Questions
2.
The change in temperature when a gas is compressed or when it expands against a piston is due to
the increase or decrease in the average s
PHYSICS 4B
PROF. HIRSCH
QUIZ 1
3 Problems
SPRING QUARTER 2014
APRIL 7th
Problem 1 (10 pts+2pts extra credit)
liquid
A cubic block of side length 10 cm and mass 100 g floats in a liquid (not water). Ha
CHAPTER 19: Heat and the First Law of Thermodynamics
Responses to Questions
26. At night, the Earth cools primarily through radiation of heat back into space. Clouds reflect energy
back to the Earth a
CHAPTER 20: Second Law of Thermodynamics
Responses to Questions
13. 1 kg of liquid iron will have greater entropy, since it is less ordered than solid iron and its molecules
have more thermal motion.
Question
A two-dimensional viscous unsteady flow takes place in the (x, y)-plabe. Ther
are no body forces. The fluid is incompressible and hsas constant density
and constant dynamic viscosity . Show
Question
Verify thet, if U is a constant, then the stream function (x, y) = U xy
represents two-dimensional inviscid flwo with no bsy forces in the region
cfw_(x, y) : (x 0), (y 0) bounded by solid wa
Question
An incompressible viscous heat-conduction fluid on constant density and
constant kinematic viscosity flows past a flat plate at y = 0. The flow is
two-dimensional. Far away from the plate, th
Question
Incompressible viscous fluid of constant density and constant kinematic
viscosity occupies the region
cfw_ < x < , < y <
above an impermeable plane situated at z = 0. This plane creates flow
Question
BRIEFLY explain the difference between the Lagrangian and Eulerian
dscripitons of flow. A fluid occupies the region D(t), and at a time t =)
position vectores in D(0) are described by X = (X,
Question
A viscous fluid of constant density and constant dynamic viscosity flows
steadily under gravity down a rigid impermeable plane. The acceleration
due to gravity is denoted by g. The plane is i
Question
A viscous fluid has constant density and constant kinematic viscosity .
Non-dimensionalise the steady Navier-Stokes equations with suitable scalings
to show that, when the Reynolds number Re
Question
A viscous incompressible fluid (having constant density and constant kinematic viscosity ) flows steadily in a pipe of constant cros-sectional are which
has its generators parallel to the z-a
Question
A viscous incompressilbe fluid with constant density and constant dynamic
viscosity flows unsteadily in the (x, y)-plane. There are no body foces.
Show that when the Reynolds number Re is muc
Question
A viscous fluid of constant density and constant kinematic viscosity flows
steadily in a two-dimensional channel < x < , 0 z h. There are
no body fporces. Thwo solid planes at z = 0 and z = h
Question
Two-dimensional fluid flow takes place in the first quadrant of the (x, y)plane. The stream function for the flow is given by
(x, y) = Cxy
where C is a positive constant.
(i) Determine the fl
Question
A solid sphere r = a is held fixed in an otherwise uniform free stream of
speed U which flows parallel to the x-axis. The REynolds number of the
stream is small. The fluid has constant densit
Question
(a) Give a brief explanation of the difference between Eulerian and Lagrangian
descriptions of a fluid flow. Denoting the Eulerian coordinates as usual
by x, prove that for any suitably smoot
Question
An axisymmetric jet of viscous incompressible fluid of consatn density and
constant kinematice viscosity is injected in the positive z-direction through
a jole at r = z = 0 into the same flui
Solutions to problems on heat engines and
Carnot cycle
Problem 1
The theoretical maximum eciency of the heat engine is given by the eciency
of a reversible heat engine. For a heat engine operating bet
Solutions to problems from kinetic theory of gases
1
Problem 1
We assume the gas is an ideal gas whose velocities are distributed according to
the Maxwell-Boltzmann distribution for the speeds f (v).