Answer :
Answer:
η=0.568
Explanation:
At inlet condition
temperature = 30 C and pressure P=1 bar
The maximum temperature = 13456 C
Compression ratio r= 12
We know that for process 1-2
[tex]\dfrac{T_2}{T_1}=r^{\gamma -1}[/tex]
[tex]\dfrac{T_2}{303}=12^{1.4 -1}[/tex]
[tex]T_2=818.68 K[/tex]
Now for process 2-3
[tex]\dfrac{T_3}{T_2}=\dfrac{V_3}{V_2}[/tex]
[tex]\dfrac{273+1345}{818.86}=\dfrac{V_3}{V_2}[/tex]
[tex]\dfrac{V_3}{V_2}=1.97[/tex]
So the cut off ratio ρ=1.97
Efficiency of diesel engine
[tex]\eta =1-\dfrac{\rho ^{\gamma}-1}{r^{\gamma -1}\gamma \left (\rho -1\right )}[/tex]
Now put the values
[tex]\eta =1-\dfrac{1.97 ^{1.4}-1}{12^{1.4-1}\times 1.4\times \left (1.97 -1\right )}[/tex]
⇒η=0.568
So the efficiency is 56.8%.
