Question

Two cyclic plants with Rankine and brayton cycle are connected is series. Supplementary fining is done before the heat exchange between the condenser of brayton cycle and boiler of Rankine cycle. The fraction of total heat supplied that is used for supplementary heating is 0.2. Efficiency of Rankine cycle and brayton cycle are 30% and 40% respectively. Overall efficiency of plant is _____ %. Take 100% efficiency for heat exchanger.

• A. 52.4

Answer 1

The correct option is A 52.4
$x=0.2=\frac{Q_3}{Q_1}$

$Q_3=$ Supplementary heat

$Q_1=$ Total heat supplied in Brayton cycle

$Q_2=$ Heat supplied in brayton cycle boiler,

$\Rightarrow Q_1=Q_2+Q_3$

$\eta =\frac{W_1+W_2}{Q_1}=\frac{{\eta }_1{Q}_2+{\eta }_2(Q_3+Q_4)}{Q_2+Q_3}$

${\eta }_1=0.4,{\eta }_2=0.3$

$Q_4=$ Heat reject from condensr at Brayton cycle.

${\eta }_1=\frac{W_1}{Q_2}=1-\frac{Q_1}{Q_2}$

$(1-{\eta }_1)=\frac{Q_4}{Q_2}$

$\left(\frac{Q_2}{Q_2+Q_3}\right)=(\frac{Q_3+Q_2}{Q_2+Q_3}-\frac{Q_3}{Q_2+Q_3})=(1-x)$

$\frac{Q_3+Q_4}{Q_2+Q_3}=\frac{Q_3}{Q_2+Q_3}+\frac{Q_4}{Q_2+Q_3}$

$=x+\frac{Q_2(1-n_1)}{Q_2+Q_3}=x+(1-n_1)(1-x)$

$\Rightarrow \eta ={\eta }_1(1-x)+{\eta }_2\times \left(\frac{Q_3+Q_4}{Q_2+Q_3}\right)$

$\eta ={\eta }_1(1-x)+{\eta }_2[x+(1-{\eta }_2)\times (1-x\left)\right]$

$\eta =0.4\times 0.8+0.3(0.2+0.6\times 0.8)$

$\eta =52.4$%