Question

The following data is for a Brayton cycle working on air.

Temperature before compression $={20}^{\circ }C$
Temperature before expansion $={1000}^{\circ }C$
Pressure ratio = 7
Regenerator effectiveness $=100\%$
If the T-s process in the combustion chamber has a linear relation then the mean temperature of heat addition is ______ ${}^{\circ }C$

• A. 728.5

Answer 1

The correct option is A 728.5

$T_1={20}^{\circ }C=293\text{K}$
$T_3={1000}^{\circ }C=1273\text{K}$
$r_p=7$
$T_2=T_1(r_p{)}^{\frac{\gamma -1}{\gamma }}=293(7{)}^{\frac{1.4-1}{1.4}}=510.88\text{K}$
$T_4=\frac{T_3}{(r_p{)}^{\frac{\gamma -1}{\gamma }}}=\frac{1273}{(7{)}^{\frac{1.4-1}{1.4}}}$
$T_4=730\text{K}$
With 100% effectiveness of regeneration
$T_4=T_5=730\text{K}$

Now it is given that $T-s$ is a straight line i.e. 5 - 3 is a straight line
$T_{\text{mean}}=\frac{Q_{\text{linear supplied}}}{(s_3-s_5)}=$ Area under T-s diagram below straight line 5 - 3
on T-s diagram
$=\frac{\frac{1}{2}(T_5+T_3)(s_3-s_5)}{(s_3-s_5)}$
$=\frac{1}{2}(730+1273)=1001.54\text{K}={728.54}^{\circ }C$