In a food processing facility, a spherical container of inner radius r1 = 40 cm, outer radius r2 = 41 cm, and thermal conductivi
ty k = 1.5 W/m·K is used to store hot water and to keep it at 100°C at all times. To accomplish this, the outer surface of the container is wrapped with a 800-W electric strip heater and then insulated. The temperature of the inner surface of the container is observed to be nearly 120°C at all times. Assuming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface temperature of the container. Also determine how much water at 100°C this tank can supply steadily if the cold water enters at 20°C
1 answer:
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Answer:
a.
y[n] = x[n] x[n-1] x[n+1]
(i) Memory-less - It is not memory-less because the given system is depend on past or future values.
(ii) Causal - It is non-casual because the present value of output depend on the future value of input.
(iii) Invertible - It is invertible and the inverse of the given system is
(iv) Stable - It is stable because for all the bounded input, output is bounded.
(v) Time invariant - It is not time invariant because the system is multiplying with a time varying function.
b.
y[n] = cos(x[n])
(i) Memory-less - It is memory-less because the given system is not depend on past or future values.
(ii) Causal - It is casual because the present value of output does not depend on the future value of input.
(iii) Invertible - It is not invertible because two or more than two input values can generate same output values .
For example - for x[n] = 0 , y[n] = cos(0) = 1
for x[n] = 2 , y[n] = cos(2
) = 1
(iv) Stable - It is stable because for all the bounded input, output is bounded.
(v) Time invariant - It is time invariant because the system is not multiplying with a time varying function.
Answer:
Work = 651,1011 kJ
Explanation:
Let´s take the car as a system in order to apply the first law of thermodynamics as follows:
Where
And considering that there is no mass transfer and that the only energy flows that interact with the system are the heat losses and the work needed to move the car we have:
Regarding the energy system we have the following:
By doing the calculations we have:
Consider that in the previous calculation, the kinetic and potential energy terms were divided by 1.000 to change the units from J to kJ.
Finally, the work needed to move the car under the required conditions is calculated as follows:
Consider that in the previous calculation, the heat loss was changed previously from BTU to kJ.