Final answer:
The heat transferred per unit mass of water as it turns from liquid to vapor in a coil, considering both the enthalpy change and the work done by water due to velocity change, is 2411.5955 kJ/kg.
Step-by-step explanation:
The student is seeking to determine the heat transferred per unit mass of water as it changes from liquid to vapor in a heating coil. To find this, we use the principle of conservation of energy, also known as the First Law of Thermodynamics, which states that the change in a system's enthalpy (ΔH) is equal to the heat added to the system minus the work done by the system:
ΔH = Q - W
Where Q is the heat transferred and W is the work done by the system. Given that the enthalpies of the inlet and outlet streams are 334.9 kJ/kg and 2,726.5 kJ/kg respectively, the change in enthalpy (ΔH) can be calculated as:
ΔH = houtlet - hinlet = 2726.5 kJ/kg - 334.9 kJ/kg = 2391.6 kJ/kg
The work done by the water due to the change in velocity can be calculated using the formula:
W = ½ m(v22 - v12), where m is the mass of the water, v1 is the inlet velocity, and v2 is the exit velocity.
In this case, the velocities are given in m/s, and we are interested in the energy per unit mass, so W becomes:
W = ½(v22 - v12)
W = ½(2002 - 32) m2s-2
Plugging in the values gives:
W = ½(40000 - 9) kgm2s-2
W = ½(39991) kgm2s-2
W = 19995.5 J/kg = 19.9955 kJ/kg
Now we can find the heat transferred by rearranging the first law of thermodynamics equation to solve for Q:
Q = ΔH + W
Q = 2391.6 kJ/kg + 19.9955 kJ/kg
Q = 2411.5955 kJ/kg
The heat transferred per unit mass of water is 2411.5955 kJ/kg.