Modern Engineering Thermodynamics

192 CHAPTER 6: First Law Open System Applications
EXAMPLE 6.7 (Continued )
Filling
valve
High-pressure liquid
water at 20.0°C and
50.0 MPa
Initially empty rigid
insulated tank
FIGURE 6.15
Example 6.7.
The unknown is the final temperature in the tank. The material is liquid water.
The final temperature in the tank immediately after it has been filled is given by Eq. (6.35) as
T final filled = T in + vp in
c
In this problem T in =20.0°C, p in = 50.0 MPa, and the specific heat of liquid water can be found in Table 3.5 as c = 4.216 kJ/kg·K.
Even though the pressure range is quite high here (0 to 50.0 MPa), it is still a good assumption to take the specific volume of
the water to be a constant at the value of v f (20.0°C) = 0.001002 m 3 /kg; the value of v (20.0°C, 50.0 MPa) from Table C.4b of
Thermodynamic Tables to accompany Modern Engineering Thermodynamics is 0.0009804 m 3 /kg, which is approximately the same
as v f (20.0°C). Then, Eq. (6.35) gives
T final filled = 20:0°C + ð0:001002 m3 /kgÞð50:0 × 10 3 kN/m 2 Þ
4:216 kN.m/kg.K
= 31:9°C
Exercises
18. An insulated, initially empty rigid container is filled with water from a water faucet in a house to a pressure of 0.700
MPa. The temperature of the water in the faucet and entering the container is 20.0°C. Determine the final temperature in
the container immediately after it has been filled. Answer: T filled = 20.2°C.
19. Determine the final temperature in the tank in Example 6.7 if it is filled with liquid mercury instead of water under the
same conditions. Use v = 7.50 × 10 −5 m 3 /kg for mercury. Answer: T filled = 20.9°C.
On the other hand, if we assume that the tank is filled with an ideal gas, then we can utilize Eq. (6.22) to get
u 2 = c v T 2 = h in = c p T in
or
T 2
filling
ideal
gas
= c p /c v
Tin = kT in (6.36)
In the case of an ideal gas, the compression process generates a considerable amount of internal energy, as the
following example illustrates.
EXAMPLE 6.8
A scuba diving air tank is filled from a 20.0°C, 1.40 MPa air supply. Neglecting the effect of any air initially in the tank and
assuming the tank is insulated during the filling process, determine the final temperature of the air in the tank immediately
after it is filled.
Solution
First, draw a sketch of the system (Figure 6.16).