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Air in an ideal diesel cycle is compressed from 3 Lit to 0.15 Lit and then it expands during constant pressure heat addition process by 0.15 Lit. The thermal efficiency (in %) of the cycle is___________.
Correct answer is '64.67'. Can you explain this answer?
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Air in an ideal diesel cycle is compressed from 3 Lit to 0.15 Lit and...
Given data:
- Initial volume (V1) = 3 Lit
- Final volume (V2) = 0.15 Lit
- Expansion volume (V3) = 0.15 Lit
Assumptions:
- The air behaves as an ideal gas.
- The combustion process is ideal and occurs at constant pressure.
- There are no heat losses during compression and expansion.
Calculation of compression ratio:
The compression ratio (CR) is defined as the ratio of the initial volume to the final volume:
CR = V1 / V2 = 3 / 0.15 = 20
Calculation of cutoff ratio:
The cutoff ratio (CO) is defined as the ratio of the expansion volume to the final volume:
CO = V3 / V2 = 0.15 / 0.15 = 1
Calculation of thermal efficiency:
The thermal efficiency (η) of the diesel cycle is given by the formula:
η = 1 - (1 / CR^(γ-1))
where γ is the specific heat ratio of air. For air, γ is approximately 1.4.
Substituting the values:
η = 1 - (1 / 20^(1.4-1))
= 1 - (1 / 20^0.4)
= 1 - (1 / 2.639)
= 1 - 0.3789
= 0.6211
To express the thermal efficiency as a percentage, multiply by 100:
η = 0.6211 * 100 = 62.11%
Conclusion:
The thermal efficiency of the ideal diesel cycle is 62.11%.
- Initial volume (V1) = 3 Lit
- Final volume (V2) = 0.15 Lit
- Expansion volume (V3) = 0.15 Lit
Assumptions:
- The air behaves as an ideal gas.
- The combustion process is ideal and occurs at constant pressure.
- There are no heat losses during compression and expansion.
Calculation of compression ratio:
The compression ratio (CR) is defined as the ratio of the initial volume to the final volume:
CR = V1 / V2 = 3 / 0.15 = 20
Calculation of cutoff ratio:
The cutoff ratio (CO) is defined as the ratio of the expansion volume to the final volume:
CO = V3 / V2 = 0.15 / 0.15 = 1
Calculation of thermal efficiency:
The thermal efficiency (η) of the diesel cycle is given by the formula:
η = 1 - (1 / CR^(γ-1))
where γ is the specific heat ratio of air. For air, γ is approximately 1.4.
Substituting the values:
η = 1 - (1 / 20^(1.4-1))
= 1 - (1 / 20^0.4)
= 1 - (1 / 2.639)
= 1 - 0.3789
= 0.6211
To express the thermal efficiency as a percentage, multiply by 100:
η = 0.6211 * 100 = 62.11%
Conclusion:
The thermal efficiency of the ideal diesel cycle is 62.11%.
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Community Answer
Air in an ideal diesel cycle is compressed from 3 Lit to 0.15 Lit and...
R = 3/0.15 = 20
Cut off ratio = ρ = v3/V2
V3 = 0.15 + 0.15 = 0.3 Lit
V2 = 0.15 Lit
ρ = 0.3/0.15 = 2
= 64.67%
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Air in an ideal diesel cycle is compressed from 3 Lit to 0.15 Lit and then it expands during constant pressure heat addition process by 0.15 Lit. The thermal efficiency (in %) of the cycle is___________.Correct answer is '64.67'. Can you explain this answer?
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