Microsoft Word - ENSY_5000_2022_Fall_HW_07.docx
ENSY 5000 Fundamentals of Energy System Integration
Homework Problem Set 7
NOTE: To solve this problem set as well as any other problem set, it will help if you draw your
system and identifying the energy component (property) changes and the energy interactions at
the boundaries. In some cases, you may need a sub system analysis to identify the energy
interactions.
In all your solutions,
clearly show your system definition with proper sketches indicating related energy flows
clearly show how you write your equations (e.g. Mass, Energy, Entropy balance, etc.)
identify relevant energy flows
use of definitions of power-energy relationships and efficiencies as needed
use of proper equation of state, or property relations as needed
clearly show your steps, assumptions, and approximations.
READING ASSIGNMENT: Read Chapters 8 of the Textbook.
General Information for the following questions
We learned in the lectures that a Carnot heat engine (power cycle) can be reversed and used as
either a heat pump or a refrigerator. In the case of a heat pump, the heat flow to the higher
temperature reservoir is the desired output and it is used to heat a room or building. In the case of
the refrigerator, the desired energy flow is the heat in from a region to be cooled. Unless otherwise
stated, for this HW set, assume
i) devices are operating for a 3‐hour period.
ii) electricity available for a green source (wind, photovoltaic, hydro) at a cost of
$0.237/kWh
iii) fuel source providing heat at temperature TH is available at a cost of $0.075/kWh.
iv) the work input is provided by electricity for the heat pump or refrigerator as needed,
v) three reservoirs are at temperatures TH = XXXXXXXXXXK (200oC), TL = XXXXXXXXXXK (20oC) and TI
= XXXXXXXXXXK (4oC) to answer the following questions.
There are 2 common efficiency metrics for energy systems. One of them is based on 1st law of
thermodynamics and the other is based on 2nd Law of Thermodynamics. The former is called
Energy Utilization Factor or 1st law efficiency which is defined as
??? ? Desired Utilized Energy OutputRequired Energy Input
The latter is called exergetic efficiency or 2nd law efficiency which is defined as
? ? ? Desired Utilized Exergy OutputRequired Exergy Input
Answer the following questions based on the definitions of these efficiency metrics.
Q1: A room that is kept at constant 20oC temperature has heat loss to the su
ounding at a rate of 20
kW. The outside (su
oundings) temperature is TI (given above). Heating is supplied to the room using
electrical heaters. Determine
A) electrical energy input to these heaters
B) cost of heating (for the given time‐period above)
C) total entropy production for this this heating system including the heat loss to su
ounding at
TI.
D) 1st law (energy) efficiency of this heating system
E) 2nd law (exergy) efficiency of this heating system
Q2: To heat the room given in question 1 above, a Carnot heat pump operating between room
temperature and outside temperature TI is used instead of an electrical heater. Electrical power input
is used to run the heat pump. Determine
A) electrical energy input to the Carnot heat pump
B) cost of heating (for the given time‐period above)
C) total entropy production for this this heating system including the heat loss to su
ounding at
TI.
D) 1st law (energy) efficiency of this heating system
E) 2nd law (exergy) efficiency of this heating system
Q3: Compare the heating systems in Q1 and Q2 for cost, entropy production, 1st and 2nd law
efficiencies. Which would you recommend? Why?
Q4: A cool storage space is to be kept constant temperature TI by removing heat at a rate of 15 kW.
Suppose a Carnot refrigeration is used by discharging heat to outside at temperature TL. Electrical
power input is used to run the refrigerator. Determine
A) electrical energy input to the Carnot refrigerator
B) cost of cooling the storage space (for the given time‐period above)
C) total entropy production for this this cooling system including the heat interactions at the high
and low temperatures.
D) 1st law (energy) performance of this cooling system considering the heat taken from storage
space is the desired output and work input of the refrigerator is the required input
E) 2nd law (exergy) efficiency of this cooling system exergy taken from storage space is the desired
output and exergy of work input of the refrigerator is the required input
Q5: For the same storage space in Q4 above, consider a heat powered refrigerator (a combination of
power and refrigeration devices). Carnot refrigeration cycle operates as in Q4, but power input comes
from a Carnot heat engine operating between a heat source at temperature at TH (given at the
eginning) and outside temperature TL. Determine
A) electrical energy input to this refrigerator
B) cost of cooling the storage space (for the given time‐period above)
C) total entropy production for this this cooling system including the heat interactions at
temperatures TH, TL and TI.
D) 1st law (energy) performance of this cooling system considering the heat taken from storage
space is the desired output and heat input of the heat engine is the required input
E) 2nd law (exergy) efficiency of this cooling system exergy taken from storage space is the desired
output and exergy of heat input of the heat engine is the required input
Q6: Compare the cooling systems in Q3 and Q4 for cost, entropy production, 1st and 2nd law
performances. Which would you recommend? Why?
Q7: An air tu
ine providing 100 kW power operates adiabatically (no heat, i.e., well insulated) at
steady state. The inlet temperature is 1350 K and inlet pressure is 11 bars. The exit temperature is 753
K and exit pressure is 1 bar. The exhaust of the tu
ine is discharged to the su
oundings where it
eventually comes into equili
ium with it. The su
ounding temperature is 290 K and pressure is 1 bar.
Treat air as an ideal gas with an ideal gas constant of Rg = 0.287 kJ/(kg K), and constant pressure
specific heat of cp = 1.005 kJ/(kg K). Ignoring kinetic and potential energy differences, determine,
A) the required mass flow rate of air through the tu
ine.
B) the rate of entropy production in the tu
ine.
C) the rate of exergy destruction in the tu
ine.
D) the rate of entropy production when the tu
ine exhaust reaches equili
ium with the su
ounding.
You can consider exhaust air goes into a virtual heat exchanger and exits the virtual heat exchanger at
the su
ounding temperature and pressure.
E) the rate of exergy destruction when the tu
ine exhaust reaches equili
ium with the su
ounding.
F) Using the above results; from an engineering design point would it be better to redesign the tu
ine
to improve its performance or to design a means to recover energy from the exhaust? Justify your
answer with the numbers you determined above.