GATE Exam > GATE Questions > The efficiency of an otto cycle is 60%. Comp...
Start Learning for Free
The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.
Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/K
- a)2590
- b)2592
Correct answer is between '2590,2592'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The efficiency of an otto cycle is 60%. Compression begins at 1 bar a...
Constant volume give 
Most Upvoted Answer
The efficiency of an otto cycle is 60%. Compression begins at 1 bar a...
Given data:
Efficiency of the Otto cycle = 60%
Initial pressure (P1) = 1 bar
Initial temperature (T1) = 27°C
Maximum pressure (P3) = 81 bar
Specific heat at constant volume (Cv) = 0.7 kJ/kg
Gas constant (R) = 0.3 kJ/kg/K
Efficiency of the Otto cycle:
The efficiency of the Otto cycle is given by the formula:
η = 1 - (1 / compression ratio)^(γ-1)
where γ is the ratio of specific heats (Cp/Cv).
We are given the efficiency as 60%. Let's substitute the values and solve for the compression ratio.
0.6 = 1 - (1 / compression ratio)^(γ-1)
Solving for compression ratio:
(1 / compression ratio)^(γ-1) = 0.4
Taking the logarithm of both sides:
(γ-1) * ln(1 / compression ratio) = ln(0.4)
ln(1 / compression ratio) = ln(0.4) / (γ-1)
1 / compression ratio = e^(ln(0.4) / (γ-1))
compression ratio = 1 / (e^(ln(0.4) / (γ-1)))
Calculating the maximum temperature (T3):
The maximum temperature (T3) can be calculated using the ideal gas equation:
P1 * V1 / T1 = P3 * V3 / T3
Since the volume remains constant in the Otto cycle, we can simplify the equation to:
P1 / T1 = P3 / T3
Solving for T3:
T3 = (P3 * T1) / P1
Calculating the maximum temperature in °C:
To convert the temperature from Kelvin to Celsius, we use the formula:
T(°C) = T(K) - 273.15
Now let's substitute the given values and calculate the maximum temperature.
T3 = (81 * (27 + 273.15)) / 1
T3 = 21987.15 K
T3(°C) = 21987.15 - 273.15
T3(°C) ≈ 21714
Conclusion:
The maximum temperature of the Otto cycle is approximately 21714°C.
Efficiency of the Otto cycle = 60%
Initial pressure (P1) = 1 bar
Initial temperature (T1) = 27°C
Maximum pressure (P3) = 81 bar
Specific heat at constant volume (Cv) = 0.7 kJ/kg
Gas constant (R) = 0.3 kJ/kg/K
Efficiency of the Otto cycle:
The efficiency of the Otto cycle is given by the formula:
η = 1 - (1 / compression ratio)^(γ-1)
where γ is the ratio of specific heats (Cp/Cv).
We are given the efficiency as 60%. Let's substitute the values and solve for the compression ratio.
0.6 = 1 - (1 / compression ratio)^(γ-1)
Solving for compression ratio:
(1 / compression ratio)^(γ-1) = 0.4
Taking the logarithm of both sides:
(γ-1) * ln(1 / compression ratio) = ln(0.4)
ln(1 / compression ratio) = ln(0.4) / (γ-1)
1 / compression ratio = e^(ln(0.4) / (γ-1))
compression ratio = 1 / (e^(ln(0.4) / (γ-1)))
Calculating the maximum temperature (T3):
The maximum temperature (T3) can be calculated using the ideal gas equation:
P1 * V1 / T1 = P3 * V3 / T3
Since the volume remains constant in the Otto cycle, we can simplify the equation to:
P1 / T1 = P3 / T3
Solving for T3:
T3 = (P3 * T1) / P1
Calculating the maximum temperature in °C:
To convert the temperature from Kelvin to Celsius, we use the formula:
T(°C) = T(K) - 273.15
Now let's substitute the given values and calculate the maximum temperature.
T3 = (81 * (27 + 273.15)) / 1
T3 = 21987.15 K
T3(°C) = 21987.15 - 273.15
T3(°C) ≈ 21714
Conclusion:
The maximum temperature of the Otto cycle is approximately 21714°C.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer?
Question Description
The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer?.
The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer?.
Solutions for The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer?, a detailed solution for The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? has been provided alongside types of The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The efficiency of an otto cycle is 60%. Compression begins at 1 bar and 27 0C. The maximum pressure is 81 bar. The maximum temperature of the cycle is ______________ 0C.Take Cv = 0.7 kJ/kg , R = 0.3 kJ/kg/Ka)2590b)2592Correct answer is between '2590,2592'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup