T5 SOLUTIONS (Waitz) a) Draw a thermodynamic cycle on p-v and T- v diagrams consisting of Leg 1-2: adiabatic expansion
Leg 2-3: constant volume heat addition
Leg 3-4: constant pressure expansion
Leg 4-1: isothermal compression
Assume that all processe
Massachusetts Institute of Technology
Physics Department
Physics 8.20
Special Relativity
IAP 2005
January 18, 2005
7:309:30 pm
Midterm
Instructions
This exam contains SIX problems pace yourself accordingly!
You have two hours for this test. Papers wil
UNIFIED ENGINEERING
Fall 2003
Ian A. Waitz
Problem T2. (Unified Thermodynamics)
Consider the helium tank from the gas-pressurized, bipropellant, 4th-stage rocket engine
from homework T1.
Assume the initial conditions at launch in the helium tank are pi =
8.251 Test
B. Zwiebach Only personal 2 page notes allowed. Test duration: 60 minutes. Problem 1. (10 points) Boundary conditions for open strings.
Consider two static D2-branes in four dimensional spacetime (ct, x1 , x2 , x3 ). The first one is at
x3 =
UNIFIED ENGINEERING
Fall 2003
Ian A. Waitz
Problem T1. (Unified Thermodynamics)
Below is a schematic diagram of a helium-pressurized, bipropellant rocket engine system
(for the fourth stage of the Peacekeeper ballistic missile). Describe the conversions o
Solution to T1 by Waitz. (Unified Thermodynamics)
Below is a schematic diagram of a helium-pressurized, bipropellant rocket engine system
(for the fourth stage of the Peacekeeper ballistic missile). Describe the conversions of
energy (internal, potential,
UNIFIED ENGINEERING
Fall 2003
Ian A. Waitz
Problem T6. (Thermodynamics)
Consider the following thermodynamic cycle. Assume all processes are quasi-static and
involve an ideal gas.
3
p
Const. volume
heat addition
adiabatic
expansion
2
isothermal
compressio
8.251 2005 Midterm Solutions
Question 1
z = x
=0
y = x
=
x = x
X 0 (, 1 )
X 1 (, 1 )
all Free
X 2 (, 1 )
X 0 (, 0),
X 1 (, 0),
X 2 (, 0),
X 3 (, 0) = a
X 3 (, 1 ) = 0
Dirichlet
Question 2
y
i
x
(a)
z z+i
F:
0y<1
M:
innite cylinder
(b)
z 2z
1
This scale
Massachusetts nstitute of Technology
Physics Department
Physics 8 20
Introduction to Special Relativity
Midterm Exam Solutions
.
IAP 2005
a) 1. The laws of physics should take the same form in all inertial
frames. 2. The speed of light c is the same in al