High School

2. the open cycle gas turbine operate on brayton cycle with pressure ratio 4.5/1. air enter the compressor at 210c and heated to 7800c at entry to the turbine. if mass flow rate is 140kg/min, determine : a) cycle efficiency(34.9%) b) wnet(211 kj/kg)492kw

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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