Download Physics 321 Final Exam May 1, `09

Physics 321 Final Exam May 1, ‘09 Name____________________________________
1. (10pts.) Calculate the volume occupied by an ideal gas at Standard Temperature
(273.15 K) and Pressure (1.0135 x 105 Pa) in m3 and liters:
2. (5 pts.) A cup contains 0.2 kg of tea and is heated to 90 oC. The specific heat
capacity of tea is ~ 1100 cal/Kkg. If the tea is allowed to cool to 20 oC calculate the
change in entropy:
Does the entropy of the tea increase or decrease (circle one) and reconcile this with
the second law of thermodynamics (use the back side of this page if necessary).
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3. (15 Pts.) Consider the three boxes below. In box A the partition separates an ideal
gas from a vacuum and in B the partition separates two non-identical gases while the
partition in Box C separates two identical ideal gases.
A
B
C
Calculate the entropy change in Box A when the partition is removed:
ΔS =
What is the entropy change when the partition is removed in Box B?
ΔS =
What is the entrophy change when the partition is removed in Box C? ΔS =
Which processes are reversible and irreversible and briefly discuss the paradox created
when the partition is removed in Box C. (use the back of the page if necessary.)
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4. (10 pts.) The temperature of the Earth’s surface is maintained by radiation from the
Sun. Use the Stefan-Boltzmann law for the energy emitted from the Sun and
reradiated from the Earth to show that the ratio of the temperature of the Earth to that
of the Sun is:
TEarth/ TSun = (RSun/2D)1/2
Where RSun is the radius of the Sun ( ~ 7 x 108 m) and D is the separation of the Earth
and Sun ( ~ 1.5 x 1011 m).
If the temperature of the Sun is ~ 5800 K, use the above equation to estimate
TEarth.
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5. (15 Pts.) In his Principia, Newton derived the speed of sound, υ, for an ideal gas
from
υ2=
Where ρ is the mass per volume , i.e., ρ = M/V.
Derive an equation for the speed of sound in which the process is isothermal (Newton):
Now derive an equation for the speed of sound in which the process is adiabatic , i.e.,
PVγ = Constant (Laplace):
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6. (5 Pts.) Circle the quantities below that are extensive thermodynamic variables:
U
V
N
S
T
ρ
μ
H
F
G
7. ( 10 Pts.) Given that ΔGo for CO is -137.2 kJ/mole and -394.4 for CO2, calculate the
ΔG for the reaction
2 CO + O2 → 2 CO2
Is this process spontaneous or non-spontaneous?
8. (10 Pts.) Define the enthalpy of a system:
Write down the defining equations for the Helmholtz free energy and Gibbs free energy
in terms of U,H, T, P, V and S (you can use the back of this page, if needed)
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9. (10 Pts.) Use Stirlings approximation to estimate the magnitude of the factorial of
Avagadro’s number, i.e. 6 x1023! = 10x, x = ?
10. (10 Pts.) Calculate the velocity of the maximum of the Maxwell-Boltzmann
velocity distribution
D(v) = (m/2πkT)3/2 4π v2 exp[-mv2/2kT]
Compare this with the speed of sound derived from Problem 5.
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Below you will find some useful relationships:
1 cal = 4.186 J
R= 8.315 J/molK
k = 1.381 x 10 -23 J/ K = 8.617 x 10-5 eV/ K
h = 6.626 x 10-34 J sec
1 atm = 1.013 bar = 1.013 x 105 N / m2
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