A boiler furnace releases 10000.000kJ of heat for each kg of fuel burned and produces dry saturated steam at 10000.000kPa from feed water at 190.000 degrees Celsius. How many kg of steam will be produced for each kg of fuel burned if the boiler had an efficiency of 69%?
ANS = kg steam/ kg of fuel
I could use some help to figure this out. Thank you.
To determine the amount of steam produced per kg of fuel burned, we need to consider the energy balance of the system and the efficiency of the boiler.
First, let's calculate the total heat energy input from the fuel burned:
Energy input from fuel = 10000.000 kJ
Since the boiler has an efficiency of 69%, we can calculate the useful heat produced as:
Useful heat produced = Energy input from fuel * Efficiency / 100
= 10000.000 kJ * 69 / 100
= 6900.000 kJ
Now, we need to calculate the heat required to raise the temperature of the feed water from 190.000 degrees Celsius to its boiling point and then convert it into steam at 10000.000 kPa.
Consider the specific heat capacity of water (Cw) = 4.18 kJ/kg°C.
Heat required to raise the temperature of 1 kg of water to its boiling point (assuming no phase change) = mass of water * Cw * temperature rise
= 1 kg * 4.18 kJ/kg°C * (100 - 190) °C
= -776.40 kJ (since the temperature is decreasing)
Now, let's determine the heat required for phase change (latent heat of vaporization) from feed water at its boiling point (100°C) to saturated steam at 10000.000 kPa.
The latent heat of vaporization of water (Hv) at atmospheric pressure (approximately) = 2256.0 kJ/kg.
Heat required for phase change = mass of water * Hv = m * 2256.0 kJ/kg
Next, we can calculate the mass of steam produced per kg of fuel burned using the energy balance equation:
Useful heat produced = heat required to raise the temperature + heat required for phase change
= -776.40 kJ + m * 2256.0 kJ
Solving for m (mass of steam produced per kg of fuel burned):
m * 2256.0 kJ = 6900.000 kJ + 776.40 kJ
m * 2256.0 kJ = 7676.40 kJ
m = 7676.40 kJ / 2256.0 kJ
Finally, the mass of steam (kg) produced per kg of fuel burned is:
mass of steam / mass of fuel = m / 1 kg of fuel
So,
kg steam/ kg of fuel = m
Calculate m using the above equation to find the answer.