Question

A motor vehicle engine operating with a diesel engine takes in atmospherics air at a temperature of 30°C and pressure of 1 bar. During combustion, the maximum obtainable temperature is 1345°C. Calculate (a) the air standard (b) thermal efficiency of this diesel engine if the compression ration is 24/2.

Answer 1

η=0.568

Step-by-step 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

`(T_2)/(T_1)=r^(\gamma -1)`

`(T_2)/(303)=12^(1.4 -1)`

`T_2=818.68 K`

Now for process 2-3

`(T_3)/(T_2)=(V_3)/(V_2)`

`(273+1345)/(818.86)=(V_3)/(V_2)`

`(V_3)/(V_2)=1.97`

So the cut off ratio ρ=1.97

Efficiency of diesel engine

`\eta =1-(\rho ^(\gamma)-1)/(r^(\gamma -1)\gamma \left (\rho -1\right ))`

Now put the values

`\eta =1-(1.97 ^(1.4)-1)/(12^(1.4-1)* 1.4* \left (1.97 -1\right ))`

⇒η=0.568

So the efficiency is 56.8%.