the exhaust gases from an oil engine are passed through a water heater. the gasses have a specific heat of 1.0467KJ/kg-K and the temperature falls from 420 degree Celsius to 150 degree Celsius is flowing through the heater. the flow being 25 Kg/min. if the water enters the heater at 40 degree Celsius and flows at the rate of 40Kg/min, find its temperature at the exit.
To find the temperature of water at the exit of the heater, we can use the energy balance equation.
First, let's calculate the heat gained by the water from the exhaust gases:
Q = mcΔT
Where:
Q = Heat gained by water (in kilojoules)
m = Mass flow rate of water (in kg/min)
c = Specific heat of water (in KJ/kg-K)
ΔT = Change in temperature of water (in Kelvin)
Given data:
m = 40 kg/min
c = The specific heat of water (approximately 4.18 KJ/kg-K)
ΔT = Final temperature of water - Initial temperature of water
Initial temperature of water = 40 degrees Celsius = 40 + 273.15 = 313.15 K
Final temperature of water = ?
Now, let's calculate the heat gained by the water:
Q = 40 * 4.18 * (Tf - 313.15)
Next, let's calculate the heat lost by the exhaust gases:
Q = mcΔT
Where:
m = Mass flow rate of exhaust gases (in kg/min)
c = Specific heat of exhaust gases (in KJ/kg-K)
ΔT = Change in temperature of exhaust gases (in Kelvin)
Given data:
m = 25 kg/min
c = Specific heat of exhaust gases (1.0467 KJ/kg-K)
ΔT = Initial temperature of exhaust gases - Final temperature of exhaust gases
Initial temperature of exhaust gases = 420 degrees Celsius = 420 + 273.15 = 693.15 K
Final temperature of exhaust gases = 150 degrees Celsius = 150 + 273.15 = 423.15 K
Now, let's calculate the heat lost by the exhaust gases:
Q = 25 * 1.0467 * (693.15 - 423.15)
Since the heat gained by the water is equal to the heat lost by the exhaust gases:
40 * 4.18 * (Tf - 313.15) = 25 * 1.0467 * (693.15 - 423.15)
Now, we can solve for Tf, the final temperature of water at the exit.