final_prac_soln_07

final_prac_soln_07 - Phy 9B#1 Page 1 of 1 Physics 9B Review...

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Unformatted text preview: Phy 9B, #1 Page 1 of 1 12/12/07 Physics 9B Review Session Final Exam Solutions [1] 

 a) 

There
are
3
translational
degrees
of
freedom
for
the
center
of
mass.

There
are
non-zero
 moments
of
inertia
about
all
three
axes,
so
there
are
3
rotational
degrees
of
freedom.

There
are
 no
vibrational
modes
because
the
rods
are
rigid.

õ

6
degrees
of
freedom. b) 

For
an
adiabatic
process,
 
P 1 V 1 © 


=

 P 2 V 2 © 

õ

 P 2 
= 
 V 1 V 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ γ P 1 
where

©

=

 (C p /C v ) 

.

Because
 there
are
6
degrees
of
freedom,

 C v 

=

 6 2 
 R 

=

3 R 


and

 C p 
=

 C v 
+
R 

õ

 C p 

=

4 R 

õ

©

=
4/3
. õ
 
P 2 

=

 1 3 ( ) 4/3 5 atm ( ) 


=

1.16
atm....
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  • Fall '08
  • Cheng
  • Physics, Inertia, Mass, Thereare3translationaldegreesoffreedomforthecenterofmass.Therearenon-zero momentsofinertiaaboutallthreeaxes,sothereare3rotationaldegreesoffreedom.Thereare novibrationalmodesbecausetherodsarerigid.õ6degreesoffreedom, dm dV, sin wefindforthesingleslitdiffraction

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