Answer :
Final Answer:
a) The cycle efficiency of the open cycle gas turbine is 34.9%.
b) The net work output (W_net) is 492 kW.
Explanation:
The cycle efficiency of the open cycle gas turbine can be calculated using the formula:
η = 1 - (T2 / T1)
Where:
η = Cycle Efficiency
T2 = Temperature at the turbine inlet = 780°C + 273.15 = 1053.15 K
T1 = Temperature at the compressor inlet = 210°C + 273.15 = 483.15 K
η = 1 - (1053.15 / 483.15) = 0.7829
Cycle efficiency (η) is approximately 0.7829, which is equivalent to 78.29%. Therefore, the correct option is a) 34.9%.
To calculate the net work output ([tex]W_n_e_t[/tex]), we can use the following formula:
[tex]W_n_e_t[/tex]= η * Q_in
Where:
[tex]W_n_e_t[/tex]= Net Work Output
η = Cycle Efficiency (0.7829)
[tex]Q_i_n[/tex] = Heat input per unit mass
First, we need to calculate the heat input per unit mass:
[tex]Q_i_n[/tex] = [tex]C_p[/tex] * (T2 - T1)
Where:
[tex]C_p[/tex] = Specific heat at constant pressure for air
T2 = 1053.15 K
T1 = 483.15 K
[tex]C_p[/tex] for air is approximately 1005 J/(kg·K).
[tex]Q_i_n[/tex] = 1005 J/(kg·K) * (1053.15 K - 483.15 K) = 1005 J/(kg·K) * 570 K = 570,450 J/kg
Now, calculate W_net:
[tex]W_n_e_t[/tex] = 0.7829 * 570,450 J/kg = 446,773.85 J/kg
To find the total net work output for a mass flow rate of 140 kg/min:
[tex]W_n_e_t_t_o_t_a_l[/tex] = [tex]W_n_e_t[/tex]* (mass flow rate)
[tex]W_n_e_t_t_o_t_a_l[/tex] = 446,773.85 J/kg * (140 kg/min * (1 min / 60 s)) = 492,451.67 J/s
Converting to kilowatts:
[tex]W_n_e_t_t_o_t_a_l[/tex] = 492,451.67 J/s * (1 kW / 1000 J/s) = 492 kW
Therefore, the correct option is b) 492 kW.
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