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In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv = 0.718 kJ/kg K, γ = 1.4
Correct answer is between '1780,1784'. Can you explain this answer?
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In an ideal Otto cycle the air in the beginning of compression is at 1...
Given:
P1 = 1 bar, T1 = 15°C = 288 K, r = 8, Q1 = 1000 kJ/kg
Q1 = Cv (T3 – T2)
Q1 = Cv(T3 – T2)
1000 = 0.718 (T3 – 521.69)
T3 = 2054.41 K = 1781.41°C
Most Upvoted Answer
In an ideal Otto cycle the air in the beginning of compression is at 1...
°C. The compression ratio is 8 and the heat addition occurs at a constant volume. The specific heat ratio of the air is 1.4.
To find:
a) pressure and temperature at the end of compression
b) pressure and temperature at the end of heat addition
c) net work done per cycle
d) thermal efficiency
Solution:
a) The ratio of volumes at the beginning and end of compression is given by the compression ratio, r = V2/V1 = 8, where V1 is the initial volume of air and V2 is the final volume of air. Since the heat addition occurs at constant volume, the pressure at the end of compression is given by:
P2 = P1 * r^γ = 1 * 8^1.4 = 26.87 bar
The temperature at the end of compression can be found using the ideal gas law:
P1V1/T1 = P2V2/T2
T2 = T1 * (P2/P1) * (V1/V2) = 15 + 273.15 * (26.87/1) * (1/8) = 710.5 K
b) Since the heat addition occurs at constant volume, the pressure and volume remain the same. Therefore:
P3 = P2 = 26.87 bar
V3 = V2 = V1/r = 0.125 V1
The temperature at the end of heat addition can be found using the first law of thermodynamics:
Q = C_v * (T3 - T2)
Q = C_v * (T3 - 710.5)
where Q is the heat added per unit mass of air and C_v is the specific heat at constant volume. The net heat added per cycle is:
Q = C_v * (T3 - 710.5) * m
where m is the mass of air in one cycle.
The net work done per cycle is given by:
W = Q - Q_out = Q - C_v * (T4 - T1) * m
where Q_out is the heat rejected per cycle and T4 is the temperature at the end of the expansion.
c) The net work done per cycle is:
W = C_v * (T3 - 710.5) * m - C_v * (T4 - 288.15) * m
where T4 can be found using the ideal gas law:
P3V3/T3 = P4V4/T4
T4 = T3 * (P4/P3) * (V3/V4) = 710.5 * (1/26.87) * (V1/0.125 V1) = 288.15 K
Substituting the values, we get:
W = C_v * (T3 - 710.5) * m - C_v * (T4 - 288.15) * m
W = C_v * (T3 - T4) * m
d) The thermal efficiency is given by:
η = W/Q_in = W/(C_v * (T3 - T2) * m)
Substituting the values, we get:
η = (C_v * (T3 - T4) * m)/(C_v * (T3 - 710.5) * m)
η = (
To find:
a) pressure and temperature at the end of compression
b) pressure and temperature at the end of heat addition
c) net work done per cycle
d) thermal efficiency
Solution:
a) The ratio of volumes at the beginning and end of compression is given by the compression ratio, r = V2/V1 = 8, where V1 is the initial volume of air and V2 is the final volume of air. Since the heat addition occurs at constant volume, the pressure at the end of compression is given by:
P2 = P1 * r^γ = 1 * 8^1.4 = 26.87 bar
The temperature at the end of compression can be found using the ideal gas law:
P1V1/T1 = P2V2/T2
T2 = T1 * (P2/P1) * (V1/V2) = 15 + 273.15 * (26.87/1) * (1/8) = 710.5 K
b) Since the heat addition occurs at constant volume, the pressure and volume remain the same. Therefore:
P3 = P2 = 26.87 bar
V3 = V2 = V1/r = 0.125 V1
The temperature at the end of heat addition can be found using the first law of thermodynamics:
Q = C_v * (T3 - T2)
Q = C_v * (T3 - 710.5)
where Q is the heat added per unit mass of air and C_v is the specific heat at constant volume. The net heat added per cycle is:
Q = C_v * (T3 - 710.5) * m
where m is the mass of air in one cycle.
The net work done per cycle is given by:
W = Q - Q_out = Q - C_v * (T4 - T1) * m
where Q_out is the heat rejected per cycle and T4 is the temperature at the end of the expansion.
c) The net work done per cycle is:
W = C_v * (T3 - 710.5) * m - C_v * (T4 - 288.15) * m
where T4 can be found using the ideal gas law:
P3V3/T3 = P4V4/T4
T4 = T3 * (P4/P3) * (V3/V4) = 710.5 * (1/26.87) * (V1/0.125 V1) = 288.15 K
Substituting the values, we get:
W = C_v * (T3 - 710.5) * m - C_v * (T4 - 288.15) * m
W = C_v * (T3 - T4) * m
d) The thermal efficiency is given by:
η = W/Q_in = W/(C_v * (T3 - T2) * m)
Substituting the values, we get:
η = (C_v * (T3 - T4) * m)/(C_v * (T3 - 710.5) * m)
η = (
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In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer?
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In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer?.
In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an ideal Otto cycle the air in the beginning of compression is at 1 bar and 15°C. The compression ratio is 8. If the heat added at constant volume process is 1000 kJ/kg, determine the maximum temperature (in °C) in the cycle. Take Cv= 0.718 kJ/kg K, γ = 1.4Correct answer is between '1780,1784'. Can you explain this answer?.
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