Final answer:
The rate at which thermal energy is being provided to the engine is approximately 333,333.33 watts, and the estimated thrust specific fuel consumption is approximately 0.065 kg/N.
Step-by-step explanation:
To calculate the rate at which thermal energy is being provided to the engine, we can use the formula:
Rate of thermal energy = Installed thrust * Velocity / Overall efficiency
Given that the installed thrust is 80 kN and the overall efficiency is 48%, we can substitute these values into the formula to find:
Rate of thermal energy = 80,000 N * (2,000 m/s) / 0.48 = 333,333.33 W
(a) The rate at which thermal energy is being provided to the engine by the fuel is approximately 333,333.33 watts.
(b) To calculate the estimated thrust specific fuel consumption, we need to divide the mass flow rate of fuel by the thrust. The mass flow rate of fuel can be calculated using the fact that thermal energy provided to the engine equals the heating value of the fuel multiplied by the mass flow rate of fuel:
2.50 x 10^14 J = Heating value of fuel * Mass flow rate of fuel
Given that the heating value of the fuel is 48 MJ/kg, we can rearrange the equation to solve for the mass flow rate of fuel:
Mass flow rate of fuel = 2.50 x 10^14 J / 48 x 10^6 J/kg = 5208.33 kg
Now we can calculate the estimated thrust specific fuel consumption by dividing the mass flow rate of fuel by the thrust:
Estimated thrust specific fuel consumption = Mass flow rate of fuel / Installed thrust = 5208.33 kg / 80,000 N = 0.065 kg/N
(b) The estimated thrust specific fuel consumption is approximately 0.065 kg/N.