Answer to Question #295552 in Molecular Physics | Thermodynamics for Harsh

Question

A gas turbine operates on a pressure ratio of 6. The inlet air temperature to the compressor

is 300 K and the temperature of air entering to the turbine is 580°C. If the volume rate of

air entering the compressor is 250 m3

/s. Calculate the net power output of the cycle. Also,

calculate the efficiency.

Answer 1

Solution;

Given;

$\lambda_T=\frac{P_3}{P_4}=6$

$T_{1_c}=300K$

Assuming;

$T_{3_T}=T_{2_c}=580°C=853K$

$V_{1_c}=250m^3/s$

Applying steady flow energy equations;

For the compressor;

$-W_c=C_pdT$

For the turbine;

$W_T=C_pdT$

Considering the turbine;

$\frac{T_4}{T_3}=(\frac{P_4}{P_3})^{\frac{k-1}{k}}$

$T_4=853(\frac{1}{6})^{\frac{0.4}{1.4}}=511.23K$

Hence;

$W_c=-1.005×(853-300)=-555.765kJ/kg$

$W_p=1.005(853-511.23)=343.47885$

$W_{net}=W_c+W_p=-555.765+343.47=-212.29kJ/kg$

Efficiency;

$\eta=\frac{212.286}{555.765}=0.382$ or $38.2$ %