Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Chapter 19, Problem 54P, part task b
I think there is an error in part task b. It is not clear how to find the final expression for T_max.
After it has been made clear that T_max = T_3, there is a description (See blue square in the attached picture part task b) which describes that an expression must substitute T_1, but the written expression applies to T_3?
In the calculation after this, there is a sudden jump to the final expression for T_max. But it's not clear how I'm going to get to the final expression? (The orange square in the attached picture of part task b)
I have includet pictures from: The task descriptions. Expert sulution to part task a, where we are given the expression, that is needet to solve part task b. And expert sulution to part task b
Transcribed Image Text:60. Gasoline engines operate ap-
proximately on the Otto cycle,
consisting of two adiabatic
and two constant-volume seg-
ments. Figure 19.25 shows
the Otto cycle for a particular
engine. (a) If the gas in the
engine has specific-heat ratio
y, find the engine's efficiency,
assuming all processes are
reversible. (b) Find the maxi-
mum temperature in terms of
FIGURE 19.25 Problem 60
the minimum temperature Tmin. (c) How does the efficiency com-
pare with that of a Carnot engine operating between the same
temperature extremes?
3p₂
P
P2-
Combustion
3
24
Adiabatic
expansion
Adiabatic
compression
V₁
V
Exhaust/intake!
s
Transcribed Image Text:(a) Expert Solution
To determine
The efficiency of the engine.
Answer to Problem 54P
The efficiency of the engine is 1-5¹-7.
Explanation of Solution
Given info: The given gasoline engine has two adiabatic and two constant volume segments. The specific heat ratio is
y. All processes are assumed to be reversible.
Write the expression for the temperature of the hot reservoir from the figure 19.24.
Th= T3 - T₂
Here,
Th is the temperature of the hot reservoir
T3 is the temperature at point 3
T2 is the temperature at point 2
3pz (= V₁)
nR
Substitute
Th
=
e
3P2 (V₁) P2 (V₁)
nR
nR
-
=
Here,
P2 is the pressure at point 2
V₁ is the volume at point 1
n is the amount of substance
R is the universal gas constant
Write the expression for the pressure of point 1 and 2 from the adiabatic compression.
P1 = P2 (²) ²
Here,
y is the specific heat ratio
Write the expression for the pressure of point 4 and 3 from the adiabatic expansion.
P4 =
3p2 (1)
Write the expression for the temperature of the cold reservoir from the figure 19.24.
Tc = T4-T₁
Here,
Te is the temperature of the cold reservoir
T4 is the temperature at point 4
T₁ is the temperature at point 1
Y
Substitute
P4V₁
nR
P₁V₁
R
for T4, 3p2 (3) for p₁, P₁ for T₁ and p2 (3) for p in the above equation.
3p2 (3) V₁ P2()'V₁
Te =
nR
nR
e = 1-
Substitute
=
Write the expression for efficiency of the engine.
= 1.
Te
Th
2p₂ V₁
5nR
Here,
e is the efficiency of the engine
2p₂V₁
5nR
2p2V1
5/nR
2p2V1
5nR
= 1-5¹-y
2p₂ V₁
5/nR
Tmax
for T3 and
(b) Expert Solution
=
Conclusion:
Therefore, the efficiency of the engine is 1 - 5¹-1.
To determine
The maximum temperature in terms of the minimum temperature.
P₂(+V₁)
nR
Answer to Problem 54P
The maximum temperature in terms of the minimum temperature is Tmax
for T₂ in the above equation.
Explanation of Solution
Write the expression for minimum temperature at the point 1.
Tmin = T₁
P2V1
5YnR
Substitute
2p₂ V₁
for Te and for Th in the above equation.
5nR
T3
Substitute for T₁ in the above equation to find the minimum temperature at point 1.
P2V1
57nR
Tmin
Write the expression for maximum temperature at the point 3.
T₁ =
max
3p2V1
5nR
=
=
3.57-¹ Tmin.
3p2V1
for T₁ in the above equation to find the minimum temperature at point 1.
5nR
3.5-¹ Tmin
Conclusion:
Therefore, the maximum temperature in terms of the minimum temperature is Tmax
=
3.5-¹ min.
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