ANP 1105 Lecture : homeostasis.doc

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ceriseshark335

24 Mar 2012

School

University of Ottawa

Department

Anatomy and Physiology

Course

ANP 1105

Professor

Jacqueline Carnegie

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Document Summary

Homeostasis homeostasis- the ability to maintain relatively stable internal conditions even though the outside world changes continuously; indicates a dynamic state of equilibrium ( a balance in which internal conditions vary but always within limits) The body is in homeostasis when its needs are adequately met and it is functioning smoothly variable- the factor or event being regulated. Adequate blood levels of vital nutrients must be continuously present. Heart activity and blood pressure must be constantly monitored and adjusted. All homeostatic control mechanisms are processes involving at least 3 components that work together: receptor. Some type of sensor that monitors the environment and responds to changes called stimuli, by sending input information to the 2nd component called the control centre along the afferent pathway (afferent = approaches the control centre: control centre. Determines the set point (the level or range at which a variable is to be maintained) It analyzes the input it receives and determines an appropriate response.

Related Questions

Situations arise in engineering when we want to control the flow rate of a solution. This solution could be pumped into a holding tank, distillation column, heat exchanger, reactor, etc. This means that the flow rate becomes a function of time. When we turn on a pump, the flow rate is (for the most part) constant. The problem is that we may want the flow rate to be very fast at first, and then very slow towards the end of the process. This is especially true in certain chemical reactors where the concentration of reactants is always important. Control systems that could handle this type of situation are very expensive. Pumps (relatively speaking) are cheap. So, having a bank of pumps will usually solve the problem. The pumps are simply turned on or off to regulate the flow. Mathematically, this amounts to taking the volumetric flow rate function and finding a piecewise-linear approximation. Suppose that, because of the application we are running, we need a flow rate given by the function ,where t is in hours and v(t) is in 100 cubic feet per hour (e.g., v(0)=1 which means that at time t=0, we need a flow rate of 1*100=100 cubic feet per hour). Find a linear approximation and a piecewise-linear approximation using first two lines and then three lines. Think about what using more lines would do to the approximation. You will need to find suitable values of t to be able to find your approximation. As a further exercise, try to find values of t for your approximation that keeps the error (i.e., the difference between the approximation and the real function v(t) ) less than 0.1.Hint: to help with this, ask yourself this question: where would more lines be useful - where the function changes a lot or where the function changes a little?]

In a circuit containing only resistors, the basic (though notnecessarily explicit) assumption is that the current reaches itssteady-state value instantly. This is not the case for a circuitcontaining inductors. Due to a fundamental property of an inductorto mitigate any "externally imposed" change in current, the currentin such a circuit changes gradually when a switch is closed oropened.
Consider a series circuit containing a resistor of resistance andan inductor of inductance connected to a source of emf andnegligible internal resistance. The wires (including the ones thatmake up the inductor) are also assumed to have negligibleresistance.
Let us start by analyzing the process that takes place after switchis closed (switch remains open). In our further analysis, lowercaseletters will denote the instantaneous values of various quantities,whereas capital letters will denote the maximum values of therespective quantities.
Note that at any time during the process, Kirchhoff's loop ruleholds and is, indeed, helpful:
.
Part A
Immediately after the switch is closed, what is the current in thecircuit?
Hint A.1
How to approach the problem
Hint not displayed
ANSWER:

zero
Answer not displayed
Part B
Immediately after the switch is closed, what is the voltage acrossthe resistor?
Hint B.1
Ohm's law
Hint not displayed
ANSWER:

zero
Answer not displayed
Part C
Immediately after the switch is closed, what is the voltage acrossthe inductor?
Hint C.1
A formula for voltage across an inductor
Hint not displayed
ANSWER:

zero
Answer not displayed
Part D
Shortly after the switch is closed, what is the direction of thecurrent in the circuit?
ANSWER:
clockwise
counterclockwise
There is no current because the inductor does not allow the currentto increase from its initial zero value.
Answer not displayed
Part E
Shortly after the switch is closed, what is the direction of theinduced EMF in the inductor?
ANSWER:
clockwise
counterclockwise
There is no induced EMF because the initial value of the current iszero.
Answer not displayed
Part F
Eventually, the process approaches a steady state. What is thecurrent in the circuit in the steady state?
ANSWER:

Answer not displayed
Part G
What is the voltage across the inductor in the steady state?
Hint G.1
Induced EMF and current
Hint not displayed
ANSWER:
zero

Answer not displayed
Part H
What is the voltage across the resistor in the steady state?
ANSWER:
zero

Answer not displayed
Part I
Now that we have a feel for the state of the circuit in its steadystate, let us obtain the expression for the current in the circuitas a function of time. Note that we can use the loop rule (goingaround counterclockwise):
.
Note as well that and . Using these equations, we can get, aftersome rearranging of the variables and making the subsitution,
.
Integrating both sides of this equation yields
.
Use this last expression to obtain an expression for . Rememberthat and that .
Express your answer in terms of , , and . You may or may not needall these variables. Use the notation exp(x) for .
ANSWER:
=
Answer not displayed
Part J
Just as in the case of R-C circuits, the steady state here is neveractually reached: The exponential functions approach their limitsasymptotically as . However, it usually does not take very long forthe value of to get very close to its presumed limiting value. Thenext several questions illustrate this point.
Note that the quantity has dimensions of time and is called thetime constant (you may recall similar terminology applied to R-Ccircuits). The time constant is often denoted by . Using , one canwrite the expression

as
.
Find the ratio of the current at time to the maximum current.
Express your answer numerically, using three significantfigures.
ANSWER:
=
Answer not displayed
Part K
Find the time it takes the current to reach 99.999% of its maximumvalue.
Express your answer numerically, in units of . Use threesignificant figures.
ANSWER:
=
Answer not displayed

Part L
Find the time it takes the current to reach 99.999% of its maximumvalue. Assume that ohms and millihenrys.
Express your answer in seconds, using three significantfigures.
ANSWER:
=
Answer not displayed
seconds
Part M
Find the time it takes the current to reach 99.999% of its maximumvalue. Assume that ohms and henrys.
Express your answer in seconds, using three significantfigures.
ANSWER:
=
Answer not displayed
seconds
Part N
What fraction of the maximum value will be reached by the currentone minute after the switch is closed? Again, assume that ohms andhenrys.
Use three significant figures in your answer.
ANSWER:
=
Answer not displayed
Now consider a different situation. After switch has been closedfor a long time, it is opened; simultaneously, switch is closed, asshown in the figure. This effectively removes the battery from thecircuit.
The questions below refer to the time immediately after switch isopened and switch is closed.
Part O
What is the direction of the current in the circuit?
ANSWER:
clockwise
counterclockwise
The current is zero because there is no EMF in the circuit.
Answer not displayed
Part P
What is happening to the magnitude of the current?
ANSWER:
The current is increasing.
The current is decreasing.
The current remains constant.
Answer not displayed
Part Q
What is the direction of the EMF in the inductor?
ANSWER:
clockwise
counterclockwise
The EMF is zero because the current is zero.
The EMF is zero because the current is constant.
Answer not displayed
Part R
Which end of the inductor has higher voltage (i.e., to which end ofthe inductor should the positive terminal of a voltmeter beconnected in order to yield a positive reading)?
Hint R.1
How to approach the problem
Hint not displayed
ANSWER:
left
right
The potentials of both ends are the same.
The answer depends on the magnitude of the time constant.
Answer not displayed
Part S
For this circuit, Kirchhoff's loop rule gives
.
Note that , since the current is decreasing. Use this equation toobtain an expression for .
Hint S.1
Initial and final conditions
Hint not displayed
Hint S.2
Let us cheat a bit
Hint not displayed
Express your answer in terms of , , and . Use exp(x) for .
ANSWER:
=
Answer not displayed

Vapor cycles
5EM - Thermodynamics
September 2010
1 The T-S diagram
The temperature-entropy diagram is an alternative to the well knownpressure-
volume diagram. Before using it to analyze different vapor cycles,we need
to understand it properly.
1. Plot the following transformations for ideal gases in a T-Sdiagram
(a) Isothermal expansion
(b) Isobaric expansion
(c) Isometric heating
(d) Reversible adiabatic expansion
(e) Irreversible adiabatic expansion
2. Repeat the last question, but this time do it for a realsubstance,
starting in the compressed liquid1 region and ending in thesuperheated
region, when possible. Indicate the boundaries of eachregion.
3. We know that under certain circumstances the area under theplot
in a P-V diagram represents the work performed during theprocess.
What does it represent in this case? Under what assumptions isyour
answer true? Compare examples 6.1 and 6.2.
2 Thermal machines
We understand by thermal machine a device capable of transformingther-
mal energy (heat) into mechanical energy (work). We already knowthat
these machines have a limited efficiency which, in the two-sourcesmodel, is
obtained by Carnotâs cycle.
(Compressed liquid is sometimes also called subcooled liquid)
2.1 Carnot cycle
This cycle, although efficient, is impractical. To begin with, theextreme
temperatures of the cycle should be within the sources temperaturesfor a
finite heat flow to exist.
1. Given the temperature of the sources, draw the cycle accordingto the
named limitation.
2. Show that this leads to lower efficiency than the theoreticallimit.
3. Assume that heat flow from/to the sources is proportional to thetem-
perature difference between them and the working fluid, anddemon-
strate that a higher power output is related to a decreasedefficiency.
2.2 Rankine cycle
Out of the several practical possibilities, Rankine cycle and itsvariations is
widely used, especially for electric power generation.
1. Draw the basic cycle in a T-S diagram and explain it.
2. What does the efficiency of the cycle depend on? Comparewith
Carnotâs.
3. What are the differences between the ideal cycle and the realone?
4. Describe how it is modified by superheating and/or reheating.Explain
te benefits.
2.3 Problems
After answering the previous questions solve the followingexercises from the
book: 8.2, 8.4, 8.5, 8.13, 8.19, 8.20
3 Frigorific machines
3.1 Reverse Carnot cycle
We have already studied Carnot cycle in detail as the ideal thermalmachine.
Now we will take is as the starting point to understand thecharacteristics
of frigorific machines.
1. Draw the ideal cycle in a T-S diagram and explain it.
2. Show that this cycle has a theoretical efficiency Ã =Tcold/Thot-Tcold
3. What are the difficulties in implementing such cycle in actualdevices?
3.2 Actual refrigerators
1. Why is the turbine replaced by an expansion valve in mostcases?
2. Plot the actual cycle and explain the differences with the idealcase.
3. How do cascade and multistage systems improve the performanceof
the refrigerator?
4. What aspects are important in the choice of a refrigerant fluid?Justify
3.3 Problems
After answering the previous questions solve the followingexercises from the
book: 10.2 10.7, 10.8, 10.9, 10.22, 10.23 10.1D

ANP 1105 Lecture : homeostasis.doc

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