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Air enters into an engine cylinder at a pressure of 100 kPa and temperature of 300 K in the suction stroke of an ideal Otto cycle. The cylinder clearance volume is 600 cm3 and compression ratio is 8:1. The expansion stroke of the cycle is polytropic in nature. The pressure at the beginning of the expansion stroke is 10 MPa and the temperature at the end of the expansion stroke is 1800 K. The polytropic exponent of the expansion stroke is _.?
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Air enters into an engine cylinder at a pressure of 100 kPa and temper...
Solution:

Given:


  • Air pressure at suction stroke P1 = 100 kPa

  • Air temperature at suction stroke T1 = 300 K

  • Cylinder clearance volume V1 = 600 cm3

  • Compression ratio r = 8:1

  • Pressure at the beginning of expansion stroke P3 = 10 MPa

  • Temperature at the end of expansion stroke T4 = 1800 K



Calculation:


  • Volume at the beginning of compression stroke V2 = V1/r = 75 cm3

  • Temperature at the end of compression stroke T2 = T1*(r^0.4) = 935.5 K (assuming gamma = 1.4)

  • Pressure at the end of compression stroke P2 = P1*(r^1.4) = 1013.18 kPa (assuming gamma = 1.4)

  • Pressure at the end of the expansion stroke P4 = P3*(V3/V4)^gamma = 220.7 kPa (assuming gamma = 1.4)

  • Volume at the end of the expansion stroke V4 = V1*(r^(gamma-1))/(r^gamma) = 89.06 cm3 (assuming gamma = 1.4)

  • Volume at the beginning of the expansion stroke V3 = V4*(P4/P3)^1/gamma = 268.3 cm3 (assuming gamma = 1.4)

  • Work done during the cycle = [(P4*V4 - P1*V1) - (P3*V3 - P2*V2)]/(gamma - 1) = 131.08 kJ/kg (assuming gamma = 1.4)

  • From the first law of thermodynamics, Q = W + (U4 - U1)

  • For an ideal gas, U = Cv*T, where Cv is the specific heat at constant volume

  • Change in internal energy U4 - U1 = Cv*(T4 - T1)

  • Heat supplied to the system Q = 131.08 + Cv*(T4 - T1)

  • The polytropic exponent of the expansion stroke n is given by (P3*V3^n)/(T4*V4^(n-1)) = P4/P3

  • Substituting the given values, we get n = 1.307



Answer:

The polytropic exponent of the expansion stroke is 1.307.
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Air enters into an engine cylinder at a pressure of 100 kPa and temperature of 300 K in the suction stroke of an ideal Otto cycle. The cylinder clearance volume is 600 cm3 and compression ratio is 8:1. The expansion stroke of the cycle is polytropic in nature. The pressure at the beginning of the expansion stroke is 10 MPa and the temperature at the end of the expansion stroke is 1800 K. The polytropic exponent of the expansion stroke is _.?
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Air enters into an engine cylinder at a pressure of 100 kPa and temperature of 300 K in the suction stroke of an ideal Otto cycle. The cylinder clearance volume is 600 cm3 and compression ratio is 8:1. The expansion stroke of the cycle is polytropic in nature. The pressure at the beginning of the expansion stroke is 10 MPa and the temperature at the end of the expansion stroke is 1800 K. The polytropic exponent of the expansion stroke is _.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Air enters into an engine cylinder at a pressure of 100 kPa and temperature of 300 K in the suction stroke of an ideal Otto cycle. The cylinder clearance volume is 600 cm3 and compression ratio is 8:1. The expansion stroke of the cycle is polytropic in nature. The pressure at the beginning of the expansion stroke is 10 MPa and the temperature at the end of the expansion stroke is 1800 K. The polytropic exponent of the expansion stroke is _.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air enters into an engine cylinder at a pressure of 100 kPa and temperature of 300 K in the suction stroke of an ideal Otto cycle. The cylinder clearance volume is 600 cm3 and compression ratio is 8:1. The expansion stroke of the cycle is polytropic in nature. The pressure at the beginning of the expansion stroke is 10 MPa and the temperature at the end of the expansion stroke is 1800 K. The polytropic exponent of the expansion stroke is _.?.
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