"my eyes cause me grief
at the fate of all the daughters of my city."
It has been two months since my determination, but I have not quite lived up to my word. More and more of my friends are slipping away to worldliness. Porn, LGBT, casual relationships, hangovers.. how could they? Only three years ago we were innocent as can be. Today they cause me grief.
This is not something that crosses their minds. Even one friend of mine sees my concern as needless depression. What they do not see is that sin is a matter of eternal life and eternal death.
If I cared enough I would have stopped them, but I was more worried about being ousted from respect. I was afraid of being annoying, eccentric, moralistic. I was afraid of being abhorred, despised, shunned. I should have known that I would be more afraid of losing my peers to the devil.
How could I be so selfish? There I was, witnessing acts of sin - acts of spiritual suicide - yet I did nothing. How can I call myself a friend? How can I say my farewells while worried sick? How lousy I am..
I bore no such grief until I saw it. How blind I was. Everyone was slipping away while I enjoyed my delusions of innocence. They have sunken deep into the mud. My nearsightedness led to this. This is the fate of my people, and I must behold the result of my own carelessness.
There are only three months left if I am to do anything about it. Please God, give me the right words. For them, and for me too. If not, I will never be able to move on with my heart at ease. How else can I unsee grief?
Sunday 28 February 2016
Convergence
Prerequisite: calculus
Following Infinite Series, it is of interest to note the values of x that make the power series converge. This range of values is the interval of convergence. The radius of convergence is the value measuring from the center to either boundary. Usually the radius is one of three possibilities: center ± remainder, all real numbers, or center. Remainders are listed accordingly.
There are many ways to test for convergence, the simplest of which is the nth term test. The function a(n) must approach zero in order for the series to stop growing. The direct comparison test compares p(n) with another function of known result. It is almost a form of sandwich theorem. Note that p(n) must not have negative terms.
The ratio test sets two consecutive terms of p(n) as a ratio to show whether p(n) increases of decreases, which can then be used to conclude whether the series converges or not. Note again that p(n) must not have negative terms.
The absolute convergence test. Think about it.
The integral test sets the function p(n) as an improper integral. If the improper integral diverges then the series diverges (and p(n) must not have negative terms). The p series test is a strange one to conceptualize (has nothing to do with p(n)). A value of p = 1 makes the series grow incredibly slowly, and anything larger than one even by a bit makes the series decrease.
The limit comparison test is a combination of direct comparison test and ratio test.
When the series flips between addition and subtraction, it is an alternating series. The alternating series test looks for all three conditions in order for a series to be considered convergent. It is worth noting that if the alternating series does converge, the truncation error applies here as well.
Testing convergence is like using a magical telescope to see infinity~
Following Infinite Series, it is of interest to note the values of x that make the power series converge. This range of values is the interval of convergence. The radius of convergence is the value measuring from the center to either boundary. Usually the radius is one of three possibilities: center ± remainder, all real numbers, or center. Remainders are listed accordingly.
There are many ways to test for convergence, the simplest of which is the nth term test. The function a(n) must approach zero in order for the series to stop growing. The direct comparison test compares p(n) with another function of known result. It is almost a form of sandwich theorem. Note that p(n) must not have negative terms.
The ratio test sets two consecutive terms of p(n) as a ratio to show whether p(n) increases of decreases, which can then be used to conclude whether the series converges or not. Note again that p(n) must not have negative terms.
The absolute convergence test. Think about it.
The integral test sets the function p(n) as an improper integral. If the improper integral diverges then the series diverges (and p(n) must not have negative terms). The p series test is a strange one to conceptualize (has nothing to do with p(n)). A value of p = 1 makes the series grow incredibly slowly, and anything larger than one even by a bit makes the series decrease.
The limit comparison test is a combination of direct comparison test and ratio test.
When the series flips between addition and subtraction, it is an alternating series. The alternating series test looks for all three conditions in order for a series to be considered convergent. It is worth noting that if the alternating series does converge, the truncation error applies here as well.
There are two types of convergences. If you were to rearrange the order of the terms in an absolutely convergent series, it will not make a difference. However, the rearranging the terms in a conditionally convergent series will result in anything. You can make any sum with it~
Here is a nice systematic guide for testing convergence:
Testing convergence is like using a magical telescope to see infinity~
Infinite Series
Prerequisite: calculus
This is an infinite series:
[k, ∞] ∑a(k) = a1 + a2 + a3 .. + a∞
Sorry for the type. Here:
Here is a basic review of sequences and series. The sum of infinite geometric series will be incredibly important~
The bulk of investigating infinite series is about the power series. This is merely the sum of infinite geometric series, previously notated as [1, ∞] ∑ar^(n-1). Evaluating this sum gives c/(1-x), previously known as a/(1-r). You can have "x centered at a", notated as "x = a". The term "a" is essentially your x shift from the origin. We will come to understand the purpose later.
There are some fancy tricks you can do with the power series.. differentiate and integrate~ You can apply it to the notation itself, or expand a finite sum into its additions and differentiate / integrate term by term as you would a very long function.
The power series is all very well for polynomials and geometric sums, but for others we need to use the Taylor series:
This is merely the power series, having cn replaced with "the k order derivative of f(x) divided by k factorial". The purpose of all this can be better understood with a graph:
Say f(x) = e^x like in this graph. Pn(x) denotes an n degree Taylor polynomial, or a partial sum of f(x), or an approximation of f(x). An infinite sum gives you f(x), so the greater the n of Pn(x), the closer it approximates f(x). The series represented in this graph is centered at zero so that Pn(x) hugs f(x) at x = 0 (any series centered at zero is a Maclaurin series). It can be centered elsewhere to approximate some value far from the y axis. You might want to revisit power series with this in mind~
Since the polynomial Pn(x) is only a finite segment of the infinite function f(x), the excluded part makes the truncation error. The remainder Rn(x) of Pn(x) is the next order term. To put a number to it, the remainder estimation replaces f^(n+1)(c) with a larger version Mr^(n+1) that covers the interval [x, a].
Series and functions clash - funeries~
This is an infinite series:
[k, ∞] ∑a(k) = a1 + a2 + a3 .. + a∞
Sorry for the type. Here:
Here is a basic review of sequences and series. The sum of infinite geometric series will be incredibly important~
The bulk of investigating infinite series is about the power series. This is merely the sum of infinite geometric series, previously notated as [1, ∞] ∑ar^(n-1). Evaluating this sum gives c/(1-x), previously known as a/(1-r). You can have "x centered at a", notated as "x = a". The term "a" is essentially your x shift from the origin. We will come to understand the purpose later.
There are some fancy tricks you can do with the power series.. differentiate and integrate~ You can apply it to the notation itself, or expand a finite sum into its additions and differentiate / integrate term by term as you would a very long function.
The power series is all very well for polynomials and geometric sums, but for others we need to use the Taylor series:
This is merely the power series, having cn replaced with "the k order derivative of f(x) divided by k factorial". The purpose of all this can be better understood with a graph:
Say f(x) = e^x like in this graph. Pn(x) denotes an n degree Taylor polynomial, or a partial sum of f(x), or an approximation of f(x). An infinite sum gives you f(x), so the greater the n of Pn(x), the closer it approximates f(x). The series represented in this graph is centered at zero so that Pn(x) hugs f(x) at x = 0 (any series centered at zero is a Maclaurin series). It can be centered elsewhere to approximate some value far from the y axis. You might want to revisit power series with this in mind~
Since the polynomial Pn(x) is only a finite segment of the infinite function f(x), the excluded part makes the truncation error. The remainder Rn(x) of Pn(x) is the next order term. To put a number to it, the remainder estimation replaces f^(n+1)(c) with a larger version Mr^(n+1) that covers the interval [x, a].
Series and functions clash - funeries~
Magnetism
Prerequisite: physics
Magnets exert fields in a way that resembles electric fields:
The qvB equation applies to a charge moving in a magnetic field. The BIL equation applies to a conductor carrying current, placed perpendicular to a magnetic field. We will only consider uniform magnetic fields.
In a qvB situation, the magnetic force can become a centripetal force when the magnetic field area is at least the size of the circle. In this example, the magnetic field goes into the page (and imagine that it is uniform all over the page).
This is the conventional notation for magnetic fields perpendicular to the page (me as in me reading this blog, and you as in you awkward blog).
A lot of perpendicularity is involved in magnetism. The first right hand rule applies to the BIL equation and the third to the qvB equation.
A magnetic field produced by a current involves the vacuum permeability constant µ0. The force exerted by one current carrying conductor on another depends on length, current and the other conductor's magnetic field. To know the direction of the force, use the second right hand rule to figure the direction of B between the conductors, then use the BIL right hand rule to figure the force.
One ampere is defined as the current in each wire that is one meter apart to produce 2E-7N for every meter of wire. Should not have used the equal sign there.
A solenoid is a coil of wire that makes a strong magnetic field inside when a current is applied. This makes an electromagnet, and an even stronger one with an iron rod inside.
The magnetic field of a solenoid can be calculated with this, where N is the number of loops.
Magnetic flux is the amount of theoretical magnetic field lines. The unit is weber (Wb), or (kgm^2)/(As^2). I am not sure what one Wb is supposed to mean, but it looks like kinetic energy over current to me.
If you are still wondering, magnetic field is in a sense the density of those lines. The unit is weber per meter square (Wb/m^2), or kg/(As^2), best left as Wb/m^2 for conceptualization.
Michael Faraday discovered that one can induce a current by changing the magnetic field on a conductor. This EMF can be described as ∆ϕ/∆t, yielding J/C, or volts. According to the magnetic flux equation there are several ways to induce EMF with magnetism:
1) change magnitude of magnetic field
2) change effective area of magnetic field
3) change angle of effective area
4) change effective magnetic flux on conductor (move)
Lenz's law is almost Newton's law for magnetic flux. It can be used to determine which way an induced current will run.
Below is just a nice thing to know: since changing magnetic flux induces a current, it induces an electric field to produce the current.
Magnets exert fields in a way that resembles electric fields:
One piece of magnet has little magnetic domains within itself, domains with more or less the same electron spin. A ferromagnetic metal such as iron, cobalt, and nickel have magnetic domains that do not cancel each other out, causing an uneven distribution of charge, and so it is a magnet. Hard magnets have more consistent magnetic domains, so they can be used to stroke other metals to make more magnets.
The qvB equation applies to a charge moving in a magnetic field. The BIL equation applies to a conductor carrying current, placed perpendicular to a magnetic field. We will only consider uniform magnetic fields.
In a qvB situation, the magnetic force can become a centripetal force when the magnetic field area is at least the size of the circle. In this example, the magnetic field goes into the page (and imagine that it is uniform all over the page).
This is the conventional notation for magnetic fields perpendicular to the page (me as in me reading this blog, and you as in you awkward blog).
A lot of perpendicularity is involved in magnetism. The first right hand rule applies to the BIL equation and the third to the qvB equation.
A magnetic field produced by a current involves the vacuum permeability constant µ0. The force exerted by one current carrying conductor on another depends on length, current and the other conductor's magnetic field. To know the direction of the force, use the second right hand rule to figure the direction of B between the conductors, then use the BIL right hand rule to figure the force.
One ampere is defined as the current in each wire that is one meter apart to produce 2E-7N for every meter of wire. Should not have used the equal sign there.
A solenoid is a coil of wire that makes a strong magnetic field inside when a current is applied. This makes an electromagnet, and an even stronger one with an iron rod inside.
The magnetic field of a solenoid can be calculated with this, where N is the number of loops.
Magnetic flux is the amount of theoretical magnetic field lines. The unit is weber (Wb), or (kgm^2)/(As^2). I am not sure what one Wb is supposed to mean, but it looks like kinetic energy over current to me.
If you are still wondering, magnetic field is in a sense the density of those lines. The unit is weber per meter square (Wb/m^2), or kg/(As^2), best left as Wb/m^2 for conceptualization.
1) change magnitude of magnetic field
2) change effective area of magnetic field
3) change angle of effective area
4) change effective magnetic flux on conductor (move)
Lenz's law is almost Newton's law for magnetic flux. It can be used to determine which way an induced current will run.
Below is just a nice thing to know: since changing magnetic flux induces a current, it induces an electric field to produce the current.
Huff, there. Strange stuff. Still getting my head around.
Run Run Run
First find out about introspective.
to the edge of the world
burn burn burn
the cold lifeless torment
fight fight fight
the frozen clutch closing in
try try try
to reach that distant twinkle
leave leave leave
the dead self behind
flee flee flee
from the damp spirit
break break break
the frost creeping in
pray pray pray
to remember why the flight
wade wade wade
through a viscous resistance
see see see
a glimmer through blurry sight
hear hear hear
muted ghosts through waters
feel feel feel
all there is left and
run
The Imagery
a cold spirit chases
through thick muffling fluids
The Content
Actually I think this makes for another trilogy in this order: Feel it All, Spring Nicht, Run Run Run. How strange, that I write pessimistically for dance beats and optimistically for emo ballads.
This entry makes a good wrap up. Spring Nicht makes an appearance in "to the edge of the world" and every word that suggests "cold". Feel it All is referred to at "feel feel feel / all there is left". Where it all began.
Usually I try not to repeat words, but consecutive repetition can make an exception. I particularly like the line "pray pray pray / to remember why the flight". The worst way to lose is to forget your motive. Without a reason why, no amount of opportunity can help you win.
The Imagery
a cold spirit chases
through thick muffling fluids
The Content
Actually I think this makes for another trilogy in this order: Feel it All, Spring Nicht, Run Run Run. How strange, that I write pessimistically for dance beats and optimistically for emo ballads.
This entry makes a good wrap up. Spring Nicht makes an appearance in "to the edge of the world" and every word that suggests "cold". Feel it All is referred to at "feel feel feel / all there is left". Where it all began.
Usually I try not to repeat words, but consecutive repetition can make an exception. I particularly like the line "pray pray pray / to remember why the flight". The worst way to lose is to forget your motive. Without a reason why, no amount of opportunity can help you win.
Feel it All
First find out about introspective.
The Imagery
stroboscopic lights
bomb
destruction
grey
black
The Content
Got a feel of Riot Lights in this. There is even a bit of Sixx A.M. in there at "this is going to hurt", only because I listened to the album a lot at the time, along with Tokio Hotel.
I like the usage of countdown in this one. There is some kind of expectation, mixed with a little dread. It is also very visual, starting off in flashes of colour and quite a lot of red, then it just oozing away in the end to black.
This is an early entry. It is different in that the last line does not reflect the first. In fact, Dead Strobe was the original title. I never had a thing for parties or live concerts. Combining monstrously loud music with seizurously flashing lights makes a nightmarish headache.
flash between heartbeats
seizurous
dare to snap heartstrings
bomb ticking
countdown
five
a tangle of wires
the red or the blue
four
a network of people
them or us
three
this is going to scar
split and frayed
two
this is going to hurt
flesh and soul
one
a severed capillary
bleeds love
zero
drained of life
turning a grey pallour
as the pulse wavers
and the lights dim
in the final scene of our
dead strobe
The Imagery
stroboscopic lights
bomb
destruction
grey
black
The Content
Got a feel of Riot Lights in this. There is even a bit of Sixx A.M. in there at "this is going to hurt", only because I listened to the album a lot at the time, along with Tokio Hotel.
I like the usage of countdown in this one. There is some kind of expectation, mixed with a little dread. It is also very visual, starting off in flashes of colour and quite a lot of red, then it just oozing away in the end to black.
This is an early entry. It is different in that the last line does not reflect the first. In fact, Dead Strobe was the original title. I never had a thing for parties or live concerts. Combining monstrously loud music with seizurously flashing lights makes a nightmarish headache.
Sunday 14 February 2016
1 Timothy 2:1
"First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all people,"
The current lifestyle in which I am living now permits little thought of others. Study, sleep, repeat. I am spinning with numbers and calculations; meanwhile my grandparents are ailing, my parents are tiring, my friends are wondering, peasants are struggling, leaders are stressing, wars are waging.. Prayer gives allows me to remember this world.
It is one of few moments which I lend time to take attention off of myself. There are so many in need, of anything. But you say, does prayer make any difference? Does it? On one end there is the all giving God, while on the other there is the skeptical human. God cannot force gifts into anyone's hands. Neither can I. So does it make a difference? Maybe. Potentially.
More than anything, prayer helps me give thanks regularly. And the more I pray for others, the more I know I take things for granted. The two focuses go hand in hand. So you know, it can never do harm to pray a little more.
But the highlight of this verse is in "for all people". For me, for you, for your favourite aunt, for the nasty old lady down the street, for kings, for beggars, for pals, for strangers, for victims, for victimizers.. we are all as hopeless as one another. What goes around comes around. You better pray that people make the right decisions each day, because it will come to you sooner or later.
I do have a thing for falling into a content rhythm. Humans are this way; we never think to pray, but when some havoc breaks loose we fall to the ground and start begging like there is no tomorrow. And when things restore themselves we fall into a content rhythm again. And so the cycle continues.
So I am adding more names to my list. Even if it takes up time I would have spent on other people, it is still worth having more people receive "the touch". Or maybe I ought to make more time, or pray for more time. Pray-ception. I live with myself so much that humans are becoming less human in my mind. Pray for me too~
The current lifestyle in which I am living now permits little thought of others. Study, sleep, repeat. I am spinning with numbers and calculations; meanwhile my grandparents are ailing, my parents are tiring, my friends are wondering, peasants are struggling, leaders are stressing, wars are waging.. Prayer gives allows me to remember this world.
It is one of few moments which I lend time to take attention off of myself. There are so many in need, of anything. But you say, does prayer make any difference? Does it? On one end there is the all giving God, while on the other there is the skeptical human. God cannot force gifts into anyone's hands. Neither can I. So does it make a difference? Maybe. Potentially.
More than anything, prayer helps me give thanks regularly. And the more I pray for others, the more I know I take things for granted. The two focuses go hand in hand. So you know, it can never do harm to pray a little more.
But the highlight of this verse is in "for all people". For me, for you, for your favourite aunt, for the nasty old lady down the street, for kings, for beggars, for pals, for strangers, for victims, for victimizers.. we are all as hopeless as one another. What goes around comes around. You better pray that people make the right decisions each day, because it will come to you sooner or later.
I do have a thing for falling into a content rhythm. Humans are this way; we never think to pray, but when some havoc breaks loose we fall to the ground and start begging like there is no tomorrow. And when things restore themselves we fall into a content rhythm again. And so the cycle continues.
So I am adding more names to my list. Even if it takes up time I would have spent on other people, it is still worth having more people receive "the touch". Or maybe I ought to make more time, or pray for more time. Pray-ception. I live with myself so much that humans are becoming less human in my mind. Pray for me too~
Thursday 11 February 2016
Laws of Thermodynamics
Follow up of Heat
Prerequisite: chemistry, physics
Less on temperature, more on energy. Less on chemistry, more on physics~ Here is something we can all agree on:
The zeroeth law of dynamics was a bit of a "duh" statement that scientists overlooked. Thermal equilibrium can also be understood with concentration and electrostatic analogies. Molecules at molecular equilibrium are at uniform concentration. Charges at electrostatic equilibrium are at uniform voltage. Likewise, heat at thermal equilibrium are at uniform temperature.
There again, internal energy:
I forgot to include that heat = Q. And for internal energy, we will focus more on the format ∆U = (3/2)nR∆T.
Here is your old grandma in a brand new dress. The Law of Conservation of Energy combined with ∆U = (3/2)nR∆T, PV = nRT, and PV graphs can tell us many things~
An isothermal process is when the temperature is kept constant. Since ∆T = 0, it follows that ∆U = 0 because ∆U = (3/2)nR∆T. The graphs looks like 1/x.
An isobaric process is when the pressure is kept constant. Since ∆P = 0, W = P∆V. It is more apparent when written as "W = (F/A)(A*∆x)", bearing in mind that W = F∆x.
An isovolumetric (sometimes isochloric) process is when the volume is kept constant. Since there is no ∆x, W = 0.
The adiabatic process is when no heat flows in or out of the system. Recall that heat Q is "energy transfer due to ∆T" so "∆Q" is quite redundant. Since Q = 0, it follows that ∆U = -W because ∆U = Q - W. Here is a better adiabatic graph:
So why is it that there is a change in temperature if Q = 0? Recall that temperature is the average kinetic energy of molecules, and in the case of adiabatic processes the change in this kinetic energy is due to work.
Nothing mind boggling here. Molecules do not diffuse to a higher concentration. Charges do not move to a higher voltage. There is actually a section on Gibbs free energy in AP chemistry, which in a sense calculates the spontaneity of a reaction, but that is beyond the scope of AP physics.
Efficiencies are disappointing enough, but thermodynamics takes that disappointment one step further. Even efficiencies are not completely efficient, if you compare calculations with Q and with T.
The biggest annoyance with this law is the fact that 100% efficiency is impossible. When you convert heat to kinetic energy there is always a residue of heat at equilibrium, as seen in QH --> QL + W. Heat at equilibrium cannot do work! If you turn QL back into QH with yet inefficient work, you end up with less QH than you started with.
1) QH --> QL + W
2) QL + W --> QH' + QL'
in which QH' < QH
and QL' > QL
One day when all kinetic energy is spent and all QH falls to equilibrium, we will be in heat death. Dun, dun dun, there goes your dramatic finale! Moral of the story: kids, do not waste your kinetic energy~
Prerequisite: chemistry, physics
Less on temperature, more on energy. Less on chemistry, more on physics~ Here is something we can all agree on:
The zeroeth law of dynamics was a bit of a "duh" statement that scientists overlooked. Thermal equilibrium can also be understood with concentration and electrostatic analogies. Molecules at molecular equilibrium are at uniform concentration. Charges at electrostatic equilibrium are at uniform voltage. Likewise, heat at thermal equilibrium are at uniform temperature.
There again, internal energy:
I forgot to include that heat = Q. And for internal energy, we will focus more on the format ∆U = (3/2)nR∆T.
Here is your old grandma in a brand new dress. The Law of Conservation of Energy combined with ∆U = (3/2)nR∆T, PV = nRT, and PV graphs can tell us many things~
An isobaric process is when the pressure is kept constant. Since ∆P = 0, W = P∆V. It is more apparent when written as "W = (F/A)(A*∆x)", bearing in mind that W = F∆x.
An isovolumetric (sometimes isochloric) process is when the volume is kept constant. Since there is no ∆x, W = 0.
The adiabatic process is when no heat flows in or out of the system. Recall that heat Q is "energy transfer due to ∆T" so "∆Q" is quite redundant. Since Q = 0, it follows that ∆U = -W because ∆U = Q - W. Here is a better adiabatic graph:
So why is it that there is a change in temperature if Q = 0? Recall that temperature is the average kinetic energy of molecules, and in the case of adiabatic processes the change in this kinetic energy is due to work.
Nothing mind boggling here. Molecules do not diffuse to a higher concentration. Charges do not move to a higher voltage. There is actually a section on Gibbs free energy in AP chemistry, which in a sense calculates the spontaneity of a reaction, but that is beyond the scope of AP physics.
Efficiencies are disappointing enough, but thermodynamics takes that disappointment one step further. Even efficiencies are not completely efficient, if you compare calculations with Q and with T.
1) QH --> QL + W
2) QL + W --> QH' + QL'
in which QH' < QH
and QL' > QL
One day when all kinetic energy is spent and all QH falls to equilibrium, we will be in heat death. Dun, dun dun, there goes your dramatic finale! Moral of the story: kids, do not waste your kinetic energy~
Heat
Follow up of Temperature and Kinetic Theory
Prerequisite: chemistry
Scored me a four in AP chemistry. The first thing that tripped me up was titration (but those were good days, joking about titrating ก๋วยเตี๋ยว). Tied at second place with solubility, was calorimetry. Now I wish someone had told me this:
Sure I knew what temperature was, otherwise I would not have even gotten a three. What I did not understand was heat. It is not a difficult concept but the teacher (and the textbook) probably took it for granted and only explained temperature.
I like to think that the relation of heat and temperature is similar to that of moles and concentration, or even charge and voltage. Molecules go from high to low concentration. Charges go from high to low voltage. Likewise, heat goes from high to low temperature.
Not sure why internal energy is introduced in this chapter. Will bring this up in the next~
Latent heat is just a fancy name for heat of phase change, whether it be freezing, melting, condensing, or evapourating. It is very important because it is actually rather easy to overlook in a calculation. At least for me. And we have our old friend specific heat down there, familiar and just as important.
Physics is obsessed with rates, so there:
AP is only likely to contain conduction. The rest, again, are nice to know.
Head on to the finale of the thermal physics trilogy.. Laws of Thermodynamics~
Prerequisite: chemistry
Scored me a four in AP chemistry. The first thing that tripped me up was titration (but those were good days, joking about titrating ก๋วยเตี๋ยว). Tied at second place with solubility, was calorimetry. Now I wish someone had told me this:
Sure I knew what temperature was, otherwise I would not have even gotten a three. What I did not understand was heat. It is not a difficult concept but the teacher (and the textbook) probably took it for granted and only explained temperature.
I like to think that the relation of heat and temperature is similar to that of moles and concentration, or even charge and voltage. Molecules go from high to low concentration. Charges go from high to low voltage. Likewise, heat goes from high to low temperature.
Not sure why internal energy is introduced in this chapter. Will bring this up in the next~
Latent heat is just a fancy name for heat of phase change, whether it be freezing, melting, condensing, or evapourating. It is very important because it is actually rather easy to overlook in a calculation. At least for me. And we have our old friend specific heat down there, familiar and just as important.
Physics is obsessed with rates, so there:
AP is only likely to contain conduction. The rest, again, are nice to know.
Head on to the finale of the thermal physics trilogy.. Laws of Thermodynamics~
Temperature and Kinetic Theory
Prerequisite: chemistry
My regular physics class actually did not cover any thermal physics because most were covered in chemistry. Even so, my regular chemistry teacher was *cough cough* so I learned most stuff from AP chemistry. Here are the stuff I have left to gleam, which are mostly just equations. They are not particularly important in AP, but they are good to know~
When change in temperature causes change in length or volume. Can be written in the format on the right.
Thermal stress is a form of pressure. This is not likely to appear in AP as Young's modulus is not covered. Whatever that is. It has something to do with elasticity.
Here is another form of PV = nRT. Despite this, the classic nR form is still more common in AP than this Nk form.
I came across this vaguely in AP chemistry. Now it is a lot more clear. Geez, why did the textbook not put it this way:
where k is Boltzmann's constant.
More stuff. Nice to know, but not vital.
Also nice to know. The final answer can be in any (mass / time) unit depending on what you use in your substitution.
That symbol J.. physicists are really running out of alphabets to use! They finished the Greek letters, might as well use Chinese characters next. Sure, we have plenty of Chinese characters~
Next in the thermal physics trilogy is Heat
My regular physics class actually did not cover any thermal physics because most were covered in chemistry. Even so, my regular chemistry teacher was *cough cough* so I learned most stuff from AP chemistry. Here are the stuff I have left to gleam, which are mostly just equations. They are not particularly important in AP, but they are good to know~
When change in temperature causes change in length or volume. Can be written in the format on the right.
Thermal stress is a form of pressure. This is not likely to appear in AP as Young's modulus is not covered. Whatever that is. It has something to do with elasticity.
Here is another form of PV = nRT. Despite this, the classic nR form is still more common in AP than this Nk form.
I came across this vaguely in AP chemistry. Now it is a lot more clear. Geez, why did the textbook not put it this way:
where k is Boltzmann's constant.
More stuff. Nice to know, but not vital.
Also nice to know. The final answer can be in any (mass / time) unit depending on what you use in your substitution.
That symbol J.. physicists are really running out of alphabets to use! They finished the Greek letters, might as well use Chinese characters next. Sure, we have plenty of Chinese characters~
Next in the thermal physics trilogy is Heat
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