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

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

$\dfrac{T_2}{T_1}=r^{\gamma -1}$

$\dfrac{T_2}{303}=12^{1.4 -1}$

$T_2=818.68 K$

Now for process 2-3

$\dfrac{T_3}{T_2}=\dfrac{V_3}{V_2}$

$\dfrac{273+1345}{818.86}=\dfrac{V_3}{V_2}$

$\dfrac{V_3}{V_2}=1.97$

So the cut off ratio ρ=1.97

Efficiency of diesel engine

$\eta =1-\dfrac{\rho ^{\gamma}-1}{r^{\gamma -1}\gamma \left (\rho -1\right )}$

Now put the values

$\eta =1-\dfrac{1.97 ^{1.4}-1}{12^{1.4-1}\times 1.4\times \left (1.97 -1\right )}$

   ⇒η=0.568

So the efficiency is 56.8%.