Download CHE 301 Problem set #3

CHE 301 Problem set #8
1. An experimental arrangement for measuring the thermal conductivity of solid materials
involves the use of two long rods that are equivalent in every respect, except that one is
fabricated from a standard material of known thermal conductivity kA while the other is
fabricated from the material whose thermal conductivity kB is desired. Both rods are attached at
one end to a heat source of fixed temperature Tb, are exposed to a fluid of temperature T, and
are instrumented with thermocouples to measure the temperature at a fixed distance x1 from the
heat source. If the standard material is aluminum, with kA = 200 W/mK, and measurements
reveal values of TA = 75oC and TB = 60oC at x1 for Tb = 100oC and T = 25oC, what is the thermal
conductivity kB of the test material?
2. Police arrive at the scene of a murder and find a body and a leaking barrel of wine. The barrel
has two 6 mm bullet holes 20 cm above the floor level. Wine is still leaking, and the wine level
at the time of arrival of the police is noted to be 36 cm above the level of the bullet holes. The
total height of the wine barrel is 1.2 m, and its diameter is 0.6 m. Assuming that the barrel was
full at the time of the shooting, how much time has elapsed between the shooting and the arrival
of the police?
3. Hexamethylene tetraamnie, N4(CH2)6, is to be produced in a well-stirred semibatch reactor by
adding aqueous ammonia solution at a constant rate of 10 liters/min to an initial charge of
formalin solution:
6HCHO + 4NH3 --> N4(CH2)6 + 6H2O
The reaction is instantaneous, irreversible, and exothermic. The initial charge of formalin
solution is 2000 liters with a formaldehyde (A) concentration, CAi, of 15.0 gmol/liter. The
concentration of ammonia (B) in the solution is CB = 15.0 gmol/liter. Heat capacity of both
ammonia and formalin solution is 1000 cal/liter-oC. Heat of reaction is -74.6 kcal/gmol of
N4(CH2)6. The temperature of ammonia solution is 0oC.
a. Calculate the time required for complete consumption of formaldehyde.
b. If the initial temperature of formalin solution is at 60oC, estimate the heat to be added or
removed if the reaction mixture is to be maintained at 60oC.
c. If the initial temperature of formalin solution is at 0oC, determine the time required for
the reactor to reach 60oC for adiabatic operation.
4. We have a number of small jets that will be used in attitude control in space. These jets will be
powered by low-pressure nitrogen gas heated by an arc at the jet nozzle. Your problem deals with
the nitrogen storage system.
The nitrogen is stored in a large well-insulated, 14.5 ft3 sphere at 1 atm pressure. At take-off
the temperature is 40oF. The mass rate of flow or N2 will be constant and be equal to 0.01 lb/s.
Since the pressure inside the sphere must always be kept at 1 atm, a heater will be used inside the
sphere.
Under these conditions, what will be the temperature of the N2 in the sphere, the
instantaneous rate of heat flow to the heater, and the total heat required after 10 sec of operation?
You can assume nitrogen as an ideal gas with Cp = 7.0 Btu/lbmol.oR.
5. A long cylindrical fin is in a convection environment with a heat transfer coefficient h and an
ambient temperature T. Determine the temperature at x = 10 cm and the heat dissipated by the
fin if the base temperature of the fin is To.
T(x)
T
To
A
L
x
dx
Data: k = 230 W/moK, h = 50 W/m2oK, fin diameter = 1 cm, To = 100oC, and T = 25oC
6.
Qo
h
Q
The above figure shows a tank into which an in compressible liquid is pumped at a volumetric
flow rate Qo (ft3/s). The height of liquid in the vertical tank is h (ft). The flow rate out of the tank
is Q (ft3/s). The length of the exit line is L (ft) and its inside diameter is Dp (ft). The cylindrical
tank has an inside diameter Dt (ft). Plot the liquid level h and the velocity inside the pipe as a
function of time given an initial height ho and initial velocity Vo of the liquid in the pipe. Use the
data given in Table 1 and plot the results from t = 0 to t = 600 s.
Table 1 Gravity-flow tank data
_______________________________________________________________________
Pipe:
ID = 3 ft
Area = 7.06 ft2
Length = 2000 ft
Tank:
ID = 12 ft
Area = 113 ft2
Height = 7 ft
Initial values
h = 4.0 ft
V = 7.0 ft/s
Parameters
density = 62.4 lb/ft3 Kf = 0.0281 lbfs2/ft3