Modern Engineering Thermodynamics

252 CHAPTER 8: Second Law Closed System Applications
EXAMPLE 8.1 (Continued )
and the SB reduces to
ms ð 2 − s 1 Þ = 1 Q 2
T b rev
We know that the work mode involved in this system is of the moving boundary type
Z
pdV , but we do not know the
p − V relation for the process. Therefore, we cannot evaluate 1 W 2 directly from its auxiliary equation. However, we can solve
for 1 Q 2 from the SB, then we can find 1 W 2 from the EB:
and
Here,
and
so that
and
1Q 2 = mT b ðs 2 − s 1 Þ
1W 2 = mu ð 1 − u 2 Þ+ 1 Q 2
s 1 = s f ð50:0°CÞ = 0:7036 kJ/ ðkg⋅KÞ
s 2 = sð50:0°C and 5:00 kPaÞ = 8:4982 kJ/ ðkg⋅KÞ
u 1 = u f ð50:0°CÞ = 209:3 kJ/kg
u 2 = uð50:0°C and 5:00 kPAÞ = 2444:7 kJ/kg
1Q 2 = ð2:00 kgÞð50 + 273:15 KÞ½8:4982 − 0:7036 kJ/ ðkg⋅KÞŠ
= 5040 kJ
1W 2 = ð2:00 kg
Þð209:3 − 2444:7 kJ/kgÞ+ 5040 kJ = 569 kJ
HOW DO YOU MAKE THE ASSUMPTIONS USED TO SOLVE
EXAMPLE 8.1?
In Example 8.1, we had to deduce certain things based on information that was not explicitly given in the problem statement.
For example, we knew that the mass was constant but the specific volume increased as the water went from a saturated
liquid to a superheated vapor. Therefore, the total volume had to increase, and its expansion do moving boundary
mechanical work. This is a typical engineering situation, which requires the use of commonsense assumptions that often
come from practice and experience.
Exercises
1. Determine the heat transfer in Example 8.1 when the final state is a saturated (rather than a superheated) vapor at
50.0°C. Answer: 1 Q 2 = 4770 kJ.
2. If the system in Example 8.1 is insulated so that no heat transfer occurs and the final expansion pressure is still 5.00
kPa, determine the final temperature and quality in the system. Answer: T 2 = 32.6°C and x 2 = 2.92%.
EXAMPLE 8.2
The solar power plant shown in Figure 8.2 utilizes the thermal energy of the sun to drive a heat engine. Solar collectors with
a constant surface temperature of 200.°F absorb 100. × 10 3 Btu/h of solar energy and deliver it to the heat engine. The heat
engine rejects heat to a condenser in a river at 40.0°F. What is the maximum steady state electrical power (in kW) that can
be produced by this power plant?