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An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).
Correct answer is '4809.17'. Can you explain this answer?
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An engine running on an air standard Otto cycle has a displacement vol...
Given data:
Displacement volume (Vd) = 250 cm3 = 0.25 L
Clearance volume (Vc) = 35.7 cm3 = 0.0357 L
Pressure at the beginning of the compression process (P1) = 100 kPa
Temperature at the beginning of the compression process (T1) = 300 K
Heat transfer during constant-volume heat addition process (Q) = 800 kJ/kg
Specific heat at constant volume (Cv) = 0.718 kJ/kg.K
Ratio of specific heats at constant pressure and constant volume (γ) = 1.4
Calculating the maximum pressure in the cycle:
The Otto cycle consists of four processes: intake, compression, combustion, and exhaust. We need to calculate the maximum pressure (P3) during the combustion process.
Step 1: Calculating the compression ratio (r):
The compression ratio is the ratio of the total volume (V1) to the clearance volume (Vc).
V1 = Vd + Vc
r = V1/Vc
Substituting the given values:
V1 = 0.25 + 0.0357 = 0.2857 L
r = 0.2857/0.0357 = 8
Step 2: Calculating the temperature at the end of the compression process (T2):
We can use the ideal gas law to calculate the temperature at the end of the compression process.
P1V1/T1 = P2V2/T2
Substituting the given values:
P1 = 100 kPa = 100 kN/m2
V1 = 0.2857 L = 0.2857 m3
T1 = 300 K
γ = 1.4
Solving for T2:
T2 = T1 * (P2/P1) * (V1/V2)^(γ-1)
Since the compression process is adiabatic (Q = 0), we can use the equation:
T2 = T1 * (V1/V2)^(γ-1)
Substituting the values:
T2 = 300 * (0.2857/V2)^(1.4-1)
Step 3: Calculating the maximum pressure (P3):
During the combustion process, heat is added at constant volume. The specific heat at constant volume (Cv) and heat transfer (Q) can be used to calculate the change in temperature (ΔT).
Q = Cv * m * ΔT
Substituting the given values:
Q = 800 kJ/kg
Cv = 0.718 kJ/kg.K
We need to calculate the mass (m) and change in temperature (ΔT).
Step 3.1: Calculating the mass (m):
The mass can be calculated using the displacement volume (Vd) and the density of air (ρ).
m = ρ * Vd
Since the engine operates on an air standard cycle, we can assume air to be an ideal gas.
ρ = P1/(R * T1)
Substituting the given values:
R = 8.314 kJ/(kmol.K
Displacement volume (Vd) = 250 cm3 = 0.25 L
Clearance volume (Vc) = 35.7 cm3 = 0.0357 L
Pressure at the beginning of the compression process (P1) = 100 kPa
Temperature at the beginning of the compression process (T1) = 300 K
Heat transfer during constant-volume heat addition process (Q) = 800 kJ/kg
Specific heat at constant volume (Cv) = 0.718 kJ/kg.K
Ratio of specific heats at constant pressure and constant volume (γ) = 1.4
Calculating the maximum pressure in the cycle:
The Otto cycle consists of four processes: intake, compression, combustion, and exhaust. We need to calculate the maximum pressure (P3) during the combustion process.
Step 1: Calculating the compression ratio (r):
The compression ratio is the ratio of the total volume (V1) to the clearance volume (Vc).
V1 = Vd + Vc
r = V1/Vc
Substituting the given values:
V1 = 0.25 + 0.0357 = 0.2857 L
r = 0.2857/0.0357 = 8
Step 2: Calculating the temperature at the end of the compression process (T2):
We can use the ideal gas law to calculate the temperature at the end of the compression process.
P1V1/T1 = P2V2/T2
Substituting the given values:
P1 = 100 kPa = 100 kN/m2
V1 = 0.2857 L = 0.2857 m3
T1 = 300 K
γ = 1.4
Solving for T2:
T2 = T1 * (P2/P1) * (V1/V2)^(γ-1)
Since the compression process is adiabatic (Q = 0), we can use the equation:
T2 = T1 * (V1/V2)^(γ-1)
Substituting the values:
T2 = 300 * (0.2857/V2)^(1.4-1)
Step 3: Calculating the maximum pressure (P3):
During the combustion process, heat is added at constant volume. The specific heat at constant volume (Cv) and heat transfer (Q) can be used to calculate the change in temperature (ΔT).
Q = Cv * m * ΔT
Substituting the given values:
Q = 800 kJ/kg
Cv = 0.718 kJ/kg.K
We need to calculate the mass (m) and change in temperature (ΔT).
Step 3.1: Calculating the mass (m):
The mass can be calculated using the displacement volume (Vd) and the density of air (ρ).
m = ρ * Vd
Since the engine operates on an air standard cycle, we can assume air to be an ideal gas.
ρ = P1/(R * T1)
Substituting the given values:
R = 8.314 kJ/(kmol.K
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Community Answer
An engine running on an air standard Otto cycle has a displacement vol...
Given :
Displacement Volume (Vs) 250 cm3
Clearance Volume (Vc) 35.7 cm3
Initial pressure ( P1) = 100 kPa
Initial temperature (T1) = 300 K
Heat addition at constant volume (Qa) = 800 kJ/kg
Specific heat at constant volume (Cv) = 0.718 kJ/kg
Process 1-2 : Isentropic compression
Also,
Compression ratio
Using,
For Process 2-3 : Heat addition at constant volume
T3 = 1803.416 K
Also,
[for constant volume process]
Maximum pressure = P3 = 4809.17 kPa
Hence, the correct answer is 4809.17
Displacement Volume (Vs) 250 cm3
Clearance Volume (Vc) 35.7 cm3
Initial pressure ( P1) = 100 kPa
Initial temperature (T1) = 300 K
Heat addition at constant volume (Qa) = 800 kJ/kg
Specific heat at constant volume (Cv) = 0.718 kJ/kg
Process 1-2 : Isentropic compression
Also,
Compression ratio
Using,
For Process 2-3 : Heat addition at constant volume
T3 = 1803.416 K
Also,
[for constant volume process]Maximum pressure = P3 = 4809.17 kPa
Hence, the correct answer is 4809.17
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An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. Can you explain this answer?
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An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. 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 An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. 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 An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. Can you explain this answer?.
An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. 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 An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. 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 An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. Can you explain this answer?.
Solutions for An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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ample number of questions to practice An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).Correct answer is '4809.17'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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