SYSC 3600 – Assignment #4
1/. Recall the beer can of assignment 1. The defining equation for this system is
A
P
B
P
B
T
c
dh
h
d
U
T
c
dh
h
d
U
T
+
=
+
+
ρ
2
4
2
4
where
T
B
is the temperature of the beer and
T
A
is the ambient temperature
(a)
Hopefully you will recognize that this is a first order system.
Assuming the values
given below, what are the time constant and the static gain of the system?
U
= 0.027716982 kJ/sec m
2
”C
h
= 11.5 cm
d
= 6 cm
ρ
= 998.5 kg/m
3
c
p
= 4.20 kJ/kg ”C
(b) Suppose that at some time (
t
= 0) the beer is removed from a 3”C fridge (where it has
been for a long time) and placed in a room that is at 17”C.
The response of any system
after
t
= 0 depends entirely upon its state at
t
= 0 (the cumulative effect of the input
before
t
= 0) and the input after
t
= 0. In our case the overall response of the system will
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 John Bryant
 Derivative

Click to edit the document details