Question

A four-stroke, four cylinder SI engine has a brake thermal efficiency of $30$% and indicated power is $40kW$ at full load. At half load it has a mechanical efficiency of $65$%. What is the indicated thermal efficiency at full load?

• A. $64.1$%
• B. $46.1$%
• C. $38.1$%
• D. $19.5$%

Answer 1

The correct option is C $38.1$%

At full load:

$bp+fp=40kW$

$\text{At half load}bp=0.5\times \text{bp at full load}$

${\eta }_m=0.65=\frac{0.5\times bp}{0.5bp}\times fp$

$0.5bp=0.65(0.5,bp+fp)$

$0.5bp=0.325bp+0.65\times fp$

$fp=\frac{0.175}{0.65}\times bp=0.27bp$

Put in equation (1)

$bp+0.27bp=40$

$bp=31.5kW$

$fp=8.5kW$

$\text{Mechanical efficiency at full laod,}{\eta }_m=\frac{bp}{bp+fp}=\frac{31.5}{40}$

${\eta }_m=78.8\%$

Indicated thermal efficiency at full load

${\eta }_m=\frac{{\eta }_{nt}}{n_m}=\frac{0.3}{0.788}=0.381=38.1\%$