An operator tests the dynamic behavior of a furnace in order to identify the transfer function relating the furnace temperature (output) to the heat input. The operator performs a series of step increases / decreases in the amount of heat input and records the temperature changes in the furnace. The system is initially at steady state, and the test takes 10 h (see Fig. E5.30). Data are recorded for another 5 h after changes in the input are no longer made. 

(a) Does a visual inspection of the plots above provide enough information to determine 

(i) the order of the system transfer function
(ii) the gain
(iii) the time constant (s)
If yes, please provide the corresponding values and justify your answers. If an exact determination is not possible for some of the above, justify why and discuss what a good estimate would be. Please give the units where necessary. 

(b) How should the test procedure be modified to improve the quality of the data and make it easier (or possible) to identify the transfer function of the system from the plot?
(c) What can you qualitatively infer about the following physical parameters of the furnace (ignore the air inside):
(i) mass
(ii) density
(iii) heat capacity
(iv) furnace height
Do not perform any calculation; use words such as €œlarge,€ €œsmall,€ and €œsignificant.€ Please justify your answer.

1000 500 -500 -1000 10 15 20 0.5 F 'TTR -0.5 FniTrOn -1 5 10 15 20 Time, h Head Input, kW Temperature, K 1.