Class notes
HEAT ENGINE CYCLES
- Course
- Institution
Lecture notes of 26 pages for the course energy at University Of Manchester HISTORY 10101 (HEAT ENGINE CYCLES)
[Show more]
Seller
Follow
MonyAcademia
Content preview
1CHAPTER 1
HEAT ENGINE CYCLES
1.1 Carnot cycle
This cycle consists of two isothermal processes joined by two
adiabatic processes. It is most conveniently represented on a T-s and
p-v diagrams as follows:
Process 1-2 = isentropic expansion from T 1 to T2
Process 2-3 = isothermal heat rejection
Process 3-4 = isentropic compression from T 2 to T1
Process 4-1 = isothermal heat supply.
The cycle is completely independent of the working substance used.
T p
p4 4
P1 1
T1 4 1
P3
p2 3
T2 2
3 2
C D v
A B s
The cycle efficiency is given by
net work output
heat supplied
heat supplied heat rejected
heat supplied
, 2
T1 s B s A T2 s B s A
T1 s B s A
T1 T2 sB s A T
1 2
(1.1)
T1 sB s A T1
There is no attempt to use the Carnot cycle with gas as working
substance in practice because of two reasons:
1. The pressure of the gas changes continuously from p 4 to p1
during the isothermal heat supply and from p2 to p3 during the
isothermal heat rejection. But in practice it is much more
convenient to heat a gas at approximately constant pressure or at
constant volume.
2. The Carnot cycle, despite its high thermal efficiency, has a
small work ratio. [Work ratio is the ratio of the net work output
(area 12341) to the gross work output of the system (area
412DC4); the work done on the gas is given by 234CD2.]
Example 1.1
What is the highest possible theoretical efficiency of a heat engine
operating with a hot reservoir of furnace gases at 2000 oC when the
cooling water is available at 10oC?
Solution
T2
From Eq. (1.1) Carnot 1
T1
10 273 283
So C 1 1 0.8754
2000 273 2273
, 3
Example 1.2
A hot reservoir at 800oC and a cold reservoir at 15oC are available.
Calculate the thermal efficiency and the work ratio of a Carnot cycle
using air as the working fluid, if the maximum and minimum
pressures in the cycle are 210 bar and 1 bar.
Solution
The cycle is shown below on T-s and p-v diagrams.
Using Eq. (1.1)
T2 288
Carnot 1 1 0.732
T1 1073
In order to find the work output and the work ratio it is necessary to
find the entropy change (s1 – s4).
For an isothermal process from 4 to A,
p 210
s A s 4 R ln 4 0.287 ln = 1.535 kJ/kg K
2
p 1
At constant pressure from A to 2,
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller MonyAcademia. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $44.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
79789 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now