In 1
Problems
. chapter 20.
4, 6, 7, 20, 63, 69, 77, 71part a
(1)
1. Adiabatic Expansion
(a) Starting from dW = pdV show that the work done during an adiabatic expansion is
W=
1
[P1 V1 P2 V2 ]
1
(2)
where is the adiabatic index
(b) For an ideal gas expansion explain why dU = nCv dT . Use this to show that
U = nCv (Tf Ti )
(3)
(c) Show that for an adiabatic expansion U = W . Show that the expressions given in Eq. 2 and
Eq. 3 are consistent with this
2. Internal Combustion Engines: Briey explain how an internal combustion engine works. Draw
a PV cycle. Indicate the dierent piston strokes work in conjuction with this cycle. Whats the role of
the crankshaft and the camshaft? Extra Credit: What are the design constraints of the compression
stroke? What are the design constraints of the ignition stroke?
3. 1 Sound At a lound concert the band plays close to the threshold of pain. The sound level is
100dB one meter away from a loundspeaker which broadcasts in all directions.
(a) Determine determine the sound level 1 km away.
(b) Is this soft/loud/inaudible?
(c) What is the pressure deviation from equilibrium relative to atmospheric pressure (1 atm 1bar =
105 N/m2 remember!) one meter from the loadspeaker
4. Sound 2 The following picture shows the Pressure measured while beating two frequencies f1 and f2 .
P
Beats
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
0
2
4
6
8
10
time in units of milli sec
(a) Estimate from the gure these two frequencies. You may nd it convenient to work the next
problem rst.
(b) Show that the sum of two sin waves sin(2f1 t) and sin(2f2 t) can be written as a product of sin
and cos waves.
1