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3 years ago

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A diesel engine does not use spark plugs to ignite the fuel and air in the cylinders. Instead, the temperature required to ignit

e the fuel occurs because the pistons compress the air in the cylinders. Suppose that air at an initial temperature of 18° C is compressed adiabatically to a temperature of 733° C. Assume the air to be an ideal gas for which
γ = 7/5
Find the compression ratio, which is the ratio of the initial volume to the final volume.

1 answer:

Klio2033 [76]3 years ago

7 0

Answer:

Compression ratio = 24.42

Explanation:

From Thermodynamic,

Adiabatic Equation ⇒ TV^{γ-1} = Constant.

⇒T₁V₁^{γ-1} = T₂V₂^{γ-1} ..................(1)

Where T₁= initial Temperature, V₁ = Initial Volume, T₂ = final Temperature, V₂ = Final Volume.

Given: T₁= 18°C we convert to Kelvin(K) by adding 273.

∴ T₁= 18°C + 273 = 291K

T₂ = 733° C also,we convert to Kelvin(K) by adding 273

∴ T₂ = 733° C +273 =1046K

γ = 7/5

∴ Rearranging equation(1), we have

(T₁/T₂) = (V₂/V₁)^{γ-1}................(2)

also rearranging equation(2) we have

(V₁/V₂)^{γ-1} = (T₂/T₁).

Where (V₁/V₂) = Compression ratio.

∴ (V₁/V₂)^{(7/5)-1} =( 1046/291)

simplifying the index in the equation

I.e (7/5)-1 = (7-5 )/5 = 2/5.

(V₁/V₂)^2/5 =(1046/291)^2/5

Multiplying the power on both side of the equation by 5/2.

∴(V₁/V₂)^(2/5)×(5/2) = (1046/291)^(5/2)

⇒ V₁/V₂= (1046/291)^2.5=( 3.59)^2.5

V₁/V₂ = 24.42.

∴ Compression ratio = 24.42

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