Question

An ideal air-standard Brayton cycle operates at steady state with compressor inlet conditions of 300K

and 100kPa and a fixed turbine inlet temperature of 1700K. For the cycle, determine (a) the pressure

ratio for given thermal efficiency of 45% and (b) the net power developed

Answer 1

Answer:-

$T_1=300k \\ p_1=100k\\ T_3=1700k\\$

$r_p=(\frac{P_2}{P_1})=8$

assume air working medium

r=1.4 , $C_p=1.005 K/kg , m=1kg\\$

$process \ \ 1-2\\ \frac{T_2}{T_1}=(\frac{P_2}{P_1})^{1.4-1\over 1.4}$

$T_2=300\times (8)^{1.4-1\over 1.4}$

$\boxed{T_2=543.43K}$

process 3-4

with same formula

$T_4=938.5K$

net power=power in turbine-power in compression

Net Power (P)=$mC_p(T_3-T_4)-mC_p(T_2-T_1)$

putting values we get

$P_{net}=1\times1.005[(1700-938.5)]$

=520.66Kw m=1kg/sec

$\eta=1-\frac{1}{(r_p)^{\frac{r-1}{r}}}$

$\eta=1-\frac{1}{(8)^{\frac{1.4-1}{1.4}}}$

$\boxed{\eta_{th}=45 \%}$