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
