Modern Engineering Thermodynamics

194 CHAPTER 6: First Law Open System Applications
enthalpy (h out ≠ constant); therefore, the integral in Eq. (6.37) cannot be evaluated. However, we can devise a
way of dealing with this by defining an average specific enthalpy for the discharge flow stream as
h avg = ð1/m out Þ
where, from the conservation of mass law, m out =(m 1 − m 2 ) tank . Approximating h avg as
Eq. (6.37) becomes
Z 2
h avg = ½ðh 1 + h 2 Þ/2Š tank
1
h out dm out (6.38)
1Q 2 − h 1 ðm 1 − m 2 Þ/2 − h 2 ðm 1 − m 2 Þ/2 = m 2 u 2 − m 1 u 1
where the numerical subscripts refer exclusively to states inside the tank from this point on.
The effect of the emptying process can be more easily seen by simplifying the analysis somewhat. Let us stipulate
that the tank is insulated (so 1 Q 2 =0)andthatm 1 ≫ m 2 ≈ 0. Then, the previous equation can be rearranged
to give
h 2 = 2u 1 − h 1 (6.39)
Inthecaseofemptyingapressurizedincompressible fluid, we can write u = cT and h = cT + vp, thenEq.(6.39)
gives
T 2
emptying
incomp:
fluid
= T 1 − ðv/cÞðp 1 + p 2 Þ (6.40)
Equation (6.40) tells us that the expansion process that accompanies the emptying process of an incompressible
fluid always causes the final temperature inside the tank to be less than the initial temperature inside the tank.
In the case of emptying a pressurized ideal gas, we can write u = c v T and h = c p T, then Eq. (6.39) gives
T 2
emptying
ideal
gas
= T 1 ½ð2/kÞ− 1Š (6.41)
Since a continuous expansion process lowers the temperature of the remaining contents, this explains why pressurized
cans of paint, deodorant, and the like become very cold when they are continuously discharged.
EXAMPLE 6.9
Immediately after the scuba tank in Example 6.8 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 mass of any air remaining in
the tank when its pressure reaches atmospheric, determine the final temperature inside the tank immediately after the
tank is empty.
Solution
First, draw a sketch of the system (Figure 6.18).
Escaping air
Air T Final = ?
FIGURE 6.18
Example 6.9.
The unknown is the final temperature inside the tank immediately after the tank is emptied. The material is air.