The displacement volume of an internal combustion engine is 3 liters. The processes within each cylinder of the engine are modeled as an air-standard Diesel cycle with a cutoff ratio of 2.5. The state of the air at the beginning of compression is fixed by P1=95kPa, T1=22oC, and V1 = 3.17 liters. Determine the net work per cycle, in kJ, the power developed by the engine, in kW, and the thermal efficiency, if the cycle is executed 1000 times per min.

1) The power developed by the engine is 14705.7739 kW

2) The thermal efficiency is approximately 61.5%

Explanation:

The given parameters are;

P₁ = 95 kPa

T₁ = 22°C

V₁ = 3.17 liters

The cutoff ratio = 2.5

Displacement volume = 3 liters

The number of times the cycle is executed per minute = 1000 times per minute

We have;

The displacement volume = V₁ - V₂ = 3 l

V₁ = 3.17 l

V₂ = 3 - 3.17 = 0.17 l

Compression ratio = V₁/V₂ = 3.17/0.17 ≈ 18.65

P₂/P₁ = P₂/(95 kPa) =  (V₁/V₂)^(k) = 18.65^1.4

P₂ = (95×18.65^(1.4)) ≈ 5710.5 kPa

T₂/T₁ = (V₁/V₂)^(k - 1)

T₂/(295 K)= (18.65)^(1.4 - 1)

T₂ = 295 * (18.65)^(1.4 - 1) = 950.81 K

The cutoff ratio = V₃/V₂ = 2.5

T₃ = T₂ × V₃/V₂  = 2.5 * 950.81 K = 2377.025 K

= ×(T₃ - T₂) = 1.006 × (2377.025 - 950.81) = 1,434.77 kJ/kg

T₄ = T₃ × (V₃/V₄)^(k-1) =

Therefore,

T₄ ≈ 1064 K

=

∴ = 0.7186×(1064 - 295) = 552.6034 kJ/kg

1) The net work = - = 1,434.77 kJ/kg - 552.6034 kJ/kg ≈ 882.17 kJ/kg

The number of cycle per minute = 1000 rpm

The number of cycle per minute = 1000 rpm/60 = 16.67 cycles per second

The power developed by the engine = The number of cycles per second × The net work of the engine

Therefore;

The power developed by the engine = 16.67 cycles/second  × 882.17 kJ/kg

The power developed by the engine = 14705.7739 kW

2) Efficiency, , is given as follows;

Therefore, the thermal efficiency ≈ 61.5%.

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