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 An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (��) is 1.4, the isentropic efficiency of the compressor is  
  • a)
    0.94
  • b)
    0.81
  • c)
    0.72
  • d)
    0.63
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
An axial compressor that generates a stagnation pressure ratio of 4.0,...

Given data:
- Stagnation pressure ratio (PR) = 4.0
- Inlet stagnation temperature (T1) = 300 K
- Exit stagnation temperature (T2) = 480 K
- Ratio of specific heats (γ) = 1.4

Calculating isentropic efficiency:
The isentropic efficiency (η) of the compressor can be calculated using the formula:
η = (PR^[(γ-1)/γ] - 1) / (PR^[(γ-1)/(γ*η)] - 1)

Substitute the given values into the formula:
PR = 4.0, γ = 1.4

Calculate the actual stagnation pressure ratio:
PR_actual = T2/T1 = 480/300 = 1.6

Calculate the isentropic efficiency:
η = (4^[(1.4-1)/1.4] - 1) / (4^[(1.4-1)/(1.4*η)] - 1)
η = (4^0.286 - 1) / (4^0.214/η - 1)
η = (1.39 - 1) / (1.27/η - 1)
η = 0.39 / (0.27/η)
η = 0.39 * η / 0.27
0.27η = 0.39η
0.12η = 0.39
η = 0.39 / 0.12
η = 0.81

Therefore, the isentropic efficiency of the compressor is 0.81, which corresponds to option 'B'.
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An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (��) is 1.4, the isentropic efficiency of the compressor is a)0.94b)0.81c)0.72d)0.63Correct answer is option 'B'. Can you explain this answer?
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An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (��) is 1.4, the isentropic efficiency of the compressor is a)0.94b)0.81c)0.72d)0.63Correct answer is option 'B'. 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 An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (��) is 1.4, the isentropic efficiency of the compressor is a)0.94b)0.81c)0.72d)0.63Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (��) is 1.4, the isentropic efficiency of the compressor is a)0.94b)0.81c)0.72d)0.63Correct answer is option 'B'. Can you explain this answer?.
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