Modern Engineering Thermodynamics

6.10 Open System Unsteady State Processes 195
The final temperature immediately after the emptying process is given by Eq. (6.41) as
T final
emptying
h i
= T
2
initial
k − 1
From Example 6.8, we find that the temperature in the tank immediately after it is filled is 137.3°C or 410.4 K. This is the
initial temperature in the reverse emptying process. Again, from Table C.13b, we find for air that k = 1.4, so Eq. (6.41) gives
T final
emptying
h
= ð410: KÞ
2
1:40 − 1
i
= 176 K = −97:4°C
Since this is the reverse of the filling process, it should produce a final temperature of 20°C, the initial temperature in the filling
process. The large error here is primarily due to the use of a simplified average enthalpy [(h 1 + h 2 )/2] tank in place of a more
accurate way of evaluating Eq. (6.38). Since we have no analytic information about h out , we have no other choice if we are to
obtain a solution. The error would not be so large if the temperatures were smaller.
Exercises
23. How could you correct the problem with the error introduced by using the simple average exit enthalpy shown in
Example 6.9? Answer: Compute the average exit enthalpy over a series of small mass flow steps as the tank is emptied,
or devise a correction factor for the offending equations.
24. A small, rigid, insulated tank is filled with helium at 70.0°F. A valve is opened on the tank, and it is completely
emptied. Determine the temperature in the tank immediately after it is emptied. Answer: T final = −355°F.
25. Immediately after the scuba tank in Example 6.9 is filled, the air is released into the atmosphere through an open valve on
the top of the tank. Assuming that the emptying process is adiabatic and ignoring the effect of any air remaining in the
tank when its pressure reaches atmospheric, use Eq. (6.40) to determine the final temperature inside the tank immediately
after the tank is emptied. How does this temperature compare with the initial temperature used in Example 6.9?
Answer: T final =20.0°C, the same as the initial temperature in Example 6.9.
EXAMPLE 6.10
An insulated, rigid tank on a spacecraft contains nitrogen at 2000. psig and 70.0°F. It is desired to discharge the tank isothermally
to supply constant temperature nitrogen to the attitude control thrusters. This can be done if a portion of the discharged
nitrogen is recycled back to the tank through a heater and compressor as shown in Figure 6.19. Assuming nitrogen
to be an ideal gas and ignoring any changes in tank or flow stream kinetic and potential energies, determine
a. An expression for the ratio of recycled mass flow rate ð _m R Þ to discharge mass flow rate ð _m D Þ so that the temperature of
the nitrogen in the tank ðT T Þ is constant in time.
b. The values of _m R / _m D and _Q H for T R = 200.°F, T T = 70.0°F, _m R = 0:500 lbm/s, and _W C = −3:00 hp:
Solution
First, draw a sketch of the system (Figure 6.19).
To thrusters
m R
Nitrogen
tank
Compressor
W C
m
Recycle
D
flow
Heater loop
m out m R
Q H
FIGURE 6.19
Example 6.10, schematic.
The unknown here is to find a formula for _m R / _m D then to find its value for a specific set of conditions. Since _m R and _m D are
mass flow rates into and out of the tank, let us first apply the general energy rate balance to the tank alone (Figure 6.20)
and see what happens.
(Continued )