Respuesta :
Answer:
The amount of current supplied to heater is 47.57 A
Solution:
As per the question:
Voltage of electric heater, V = 115 V
Volume rate of flow of air, [tex]\dot{V} = 0.3\ m^{3}/s[/tex]
Initial temperature of air, T = [tex]15^{\circ}C[/tex] = 273 + 15 = 288 K
Final temperature of air, T' = [tex]30^{\circ}C[/tex] = 273 + 30 = 303 K
Initial Pressure = Final Pressure, P = 100 kPa
Specific heat of air, [tex]C_{p} = 1.005\ kJ/kg.^{\circ}C[/tex]
Gas constant, R = 0.287 [tex]kPa.m^{3}/kg.K[/tex]
Now,
To compute the amount of current supplied to the heater, we assume the steady state operation and neglecting the effects of kinetic energy and potential energy:
Specific volume, 'v' of the air at the inlet is given by:
[tex]v = \frac{RT}{P} = \frac{0.287\times 288}{100}[/tex]
[tex]v = 0.8266\ m^{3}/kg[/tex]
Mass flow rate of air can be given by:
[tex]\dot{m} = \frac{\dot{V}}{\dot{v}}[/tex]
[tex]\dot{m} = \frac{0.3}{0.8266} = 0.3629\ kg/s[/tex]
Considering the system of the pipe containing air and using the energy balance on this system:
[tex]\Delta \dot{E} = \dot{E_{in}} - \dot{E_{out}}[/tex]
[tex]\Delta \dot{E} = 0[/tex]
Therefore,
[tex]\dot{E_{i}} = \dot{E_{out}}[/tex]
[tex]\dot{E_{i}} = \dot{W} + \dot{m}h[/tex]
[tex]\dot{E_{o}} = \dot{m}h'[/tex]
Thus
[tex]\dot{W} = \dot{m}\Delta h[/tex]
Also, we know that:
[tex]\dot{W} = V\times I[/tex]
where
I = current in amperes
Now, comparing the two eqns, we get:
[tex]I = \frac{\dot{m}C_{p}{h' - h}}{V}[/tex]
[tex]I = \frac{\dot{m}C_{p}{T' - T}}{V}[/tex]
[tex]I = \frac{0.3629\times 1.005\times 10^{3}\times {303 - 288}}{115} = 47.57\ A[/tex]
