Download Problem set #2: 5

Problem set #2: 5.20, 5.21, 5.22, 5.35, 5.36, 5.37, 5.40.
5.20 One mole of CO is initially contained on one-half of a well-insulated, rigid tank. Its
temperature is 500oK. The other half of the tank is initially at vacuum. A diaphragm
separates the two compartments. Each compartment has a volume of 1 L. Suddenly, the
diaphragm ruptures. Use the van der Waals equation for any nonideal behavior. Answer
the following questions:
(a) What is cv at the initial state?
(b) Do you expect the temperature to increase, decrease, or remain constant. Justify your
answer with molecular arguments. Be specific about the nature of the forces involved.
(c) What is the temperature of the final state?
(d) What is the entropy change of the universe for this process?
5.21 A well-insulated, rigid vessel is divided into two compartments by a partition. The
volume of each compartment is 0.1 m3. One compartment initially contains 400 moles of
gas A at 300oK, and the other compartment is initially evacuated. The partition is then
removed and the gas is allowed to equilibrate. Gas A is not ideal under these
circumstances but can be described well by the following equation of state:
P=
RT
a

, where a = 42 [JKm3/mol2] and b = 3.210-5 [m3/mol].
v  b Tv 2
You may take the ideal gas heat capacity of gas A to be cv = 1.5R. Calculate the final
temperature.
5.22 Consider filling a gas cylinder with ethane from a high-pressure supply line. Before
filling, the cylinder is empty (vacuum). The valve is then opened, exposing the tank to a
3-MPa line at 500oK until the pressure of the cylinder reaches 3 MPa. The valve is then
closed. The volume of the cylinder is 50 L. For ethane, use the truncated virial equation
of state, in pressure:
z=
Pv
= 1 + B’P, where B’ =  2.810-8 [m3/J]
RT
(a) What is the temperature immediately after the valve is closed?
(b) If the cylinder then sits in storage at 293oK for a long time, what is the entropy
change of the universe (from the original unfilled, state)?
5.35 The speed of sound, Vsound [m/s], is formally equal to the partial derivative of
pressure with respect to density at constant entropy:
 P 
2
Vsound
  
   s
 P 
v 2  P 
Show that    
  where MW is the molecular weight.
MW  v  s
   s
5.36 Based on the definition in Problem 5.35, use the thermodynamic web to come up
with an expression for [Vsound] in air. What is the value of [Vsound] in air at 20oC? You may
consider air to be an ideal gas with cp = (7/2)R. Based on this result, how far away is a
bolt of lightning if you hear the thunder four seconds after you see the lightning.
5.37 Based on the definition in Problem 5.35, use the thermodynamic web to come up
with an expression for [Vsound] in water at 20oC? Use the steam tables for thermodynamic
property data of liquid water.