Cooking: temp of a warm object

Cooking means constant self-tutoring. The tutor speculates about the actual temperature of a warm object.

Yesterday I took a glass casserole dish of mac and cheese from the oven. Its baking temp was 177C.

An hour later, most of the mac and cheese had been served from the dish. Moving it, I was surprised how warm it still was to the touch.

Yet, how warm was it? I didn’t have a convenient way of measuring, so I opened a browser tab and found, whose members seem to agree that about 60C is dangerous to touch for more than a second or two.

The casserole dish wasn’t hot; rather, just surprisingly warm. I’d estimate it was about 40C.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Math: how far away is the goose?

Tutoring math, you notice that people like relatable examples. The tutor brings up his observation of a Canada goose.

Looking out over a lake in Nanaimo on Sunday morning, I saw an exceptional Canada goose swimming apart from the others.

The setting was so tranquil, even distance seemed irrelevant: I felt that, on a whim, I could suddenly scoot down to the water, plunge in, and join the goose if I wanted. Yet, how far away was it, really?

Holding my phone at 20cm, or 200mm, I observed the goose at about one-sixth of my phone’s lens port, which is 7mm across. So, to me, the goose appeared 7/6=1.17mm. Yet, a goose that prosperous would likely be about 60cm, or 600mm, from tail to breast. From optics,

object distance/image distance = object length/image length


d/200 = 600/1.17

Multiplying both sides by 200, we get

d=200(600)/1.17 = 102574mm or about 103m


Bull, John and John Farrand, Jr. The Audubon Society Field Guide to North American Birds, eastern region. New York: Alfred A. Knopf, 1977.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Astronomy: meteor, meteoroid and meteorite: what’s the difference?

Tutoring science, meteors and their kin might arise. The tutor defines meteor, meteoroid, and meteorite.

A meteor is the streak of light you might see in the sky at night, when matter travelling through space enters Earth’s atmosphere.

The rock, or whatever matter arrives, is typically travelling at high speed. The air friction it encounters in the atmosphere heats it up, usually to evaporation – but not always. However, it gets so hot it glows, which is what you observe.

The object itself, arriving in Earth’s atmosphere and glowing, is a meteoroid.

Any part of the meteoroid that lands on Earth’s surface becomes a meteorite. As I understand, meteoroids rarely manage to become meteorites.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Calculator usage: horsepower to kilowatts on the Casio fx-991ES PLUS C

Tutoring physics, you face unit conversions. The tutor shows how the Casio fx-991ES PLUS C can be used.

Inside the cover of the Casio fx-991ES PLUS C, at the bottom, is a list of unit conversions. Specifically, it indexes each conversion with a number to which the calculator refers. You’ll see, for instance,

29 hp→kW

which means that 29, entered within the conversion context, performs horsepower to kW.

Example: Using the Casio fx-991ES PLUS C, convert 296 hp to kW.


  1. I use COMP mode for this calculation: key in MODE 1
  2. Key in 296 SHIFT 8
  3. The calculator will ask for the conversion number: in this case, key in 29.
  4. Press =

Btw: for kW to hp, it’s 30 instead of 29:)


Serway, Raymond A. Physics for Scientists and Engineers WMP, second ed. Toronto: Saunders College Publishing, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Calculator usage: linear regression on the Casio fx-991ES PLUS C

Tutoring statistics, you cover linear regression. The tutor shows how to get a best-fit line on the Casio fx-991ES PLUS C.

Let’s imagine you have the following data

x y
10.1 14.2
17.3 19.5
25.4 22.9
40.0 31.8

Furthermore, you’d like to find a line of the form y=A+Bx that fits the data. Here’s how you might do it using the Casio fx-991ES PLUS C:

  1. Press Mode then 3 for Stat mode.
  2. Press 2 for y=A+Bx
  3. In the table that appears, enter the x and y values.
  4. After all the x and y values have been entered, press AC.
  5. Now, press Shift then 1.
  6. Press 5
  7. You’ll see choices for A, B, and other stats. Select the one you want, then press Enter.
  8. If, for example, you select A first and get its value, press Stat then 1 then 5 to return to the other choices. You can then choose B.


Casio fx-991ES PLUS C User’s Guide.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Electrochemistry: cell vs battery

Tutoring chemistry, the distinction between cell and battery is noted.

In electrochemistry, a cell is a single unit of electrical energy production. A cell comprises an anode and cathode, plus the ingredients and the environment needed for the chemical reaction that outputs electrical energy.

A battery comprises more than one cell connected so that they work together to deliver energy to a circuit.

People have come to refer to single cells as batteries. I’d say that the button-style power sources found in calculators, watches, etc are cells. If a calculator contains two of them, those two cells constitute a battery.

The typical car battery really is one, since it contains six cells connected.


Mortimer, Charles E. Chemistry, sixth ed. Belmont: Wadsworth, 1986.

Giancoli, Douglas C. Physics, fifth ed. New Jersey: Prentice Hall, 1998.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

AC Electricity, electronics: how a series low-pass filter works

The tutor briefly explains the low-pass filter.

This explanation draws on ideas from that of a high-pass filter (see my article here).

A low-pass filter sends along low frequencies but blocks higher ones. The one we’re looking at today has a resistor and a capacitor in series. As detailed in my article on the series high-pass filter, we have total impedance Z=(R2 + Xc2)0.5, where Xc = 1/(2πfC).

As the frequency decreases, the impedance of the capacitor increases, so its share of the voltage output rises. A low-pass filter will read the voltage across the capacitor. Relative to the input voltage for the circuit, V, its output will be

Vout/V = Xc/(R2 + Xc2)0.5

At very low frequency, the impedance of the capacitor Xc = 1/(2πfC)>>R, so

Vout/V ≈ Xc/(Xc2)0.5 = Xc/Xc = 1

The critical frequency, fc, is when Vout/V = 0.707. fc happens when R=Xc:

Vout/V = Xc/(Xc2 + Xc2)0.5 = Xc/(2Xc2)0.5 = 1/20.5 = 0.707.

To find fc we set R=Xc=1/(2πfC), then arrive at f = 1/(2πRC). A series low-pass filter with capacitor 4700pF and resistor 10kΩ will have critical frequency fc = 1/(2π*1×104*4700*10-12) = 3390Hz.


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Physics: Why is electric field between parallel plates constant, but not between two point charges?

The tutor discusses the electric field between two parallel plates, then between two point charges.

A consequence of Gauss’s Law is that, from an infinite charged plane, the electric field is constant, independent of distance, and given by

E = σ/2εο


σ = the charge density of the plane in N/m2

εο = 8.854187817 x 10-12, the permittivity of free space.

In a real capacitor, if the plates are much higher and broader than their separation, then at a point between them, collinear with their centres, the effect is probably comparable to two infinite planes of charge. In that case, the field, regardless of position along that centre line, is given by

Enet = E2 – E1

Now, a different premise: we imagine point P between two charged particles, q1 and q2, such that q1, P, and q2 are all collinear. In this situation the field at point P depends on its position between q1 and q2 and is given by

Enet = E2 – E1 = kq2/r22 – kq1/r12


k = 1/(4π*εο) = 9.0 x 109

r1 = the distance from P to q1

r2 = the distance from P to q2


Serway, Raymond A. Physics for Scientists and Engineers with modern physics, 2nd ed. Toronto: Saunders College Publishing, 1986.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Calculator usage, physics: εο: permittivity of free space constant on the Sharp el-520w

The tutor tells how to access the built-in εο constant on the Sharp el-520w.

The Sharp el-520w has 52 built-in constants relating to physics, chemistry, etc.

Here’s how to call up εο, which has value 8.85×10-12:

  1. Press the CNST key, and you’ll be asked which of constants (01-52) you require.
  2. Key in 13. You’ll see 8.854187817×10-12 appear.


Sharp Scientific Calculator Model EL-520W Operation Manual.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Chemistry, thermodynamics: temperature increase caused by compression, continued

The tutor looks more specifically into the effect of compression on gas temperature.

In my January 20 post I began about thermodynamics and the effect of compressing a gas. Today, I’ll give more specific coverage.

The temperature rise a gas experiences (without change in entropy) due to pressure is given by the formula

T2 = T1(P2/P1)[1-1/γ]


T1,T2 are initial and final temperatures

P1,P2 are initial and final temperatures

γ = Cp/Cv, where

Cp = gas specific heat at constant pressure

Cv = gas specific heat at constant volume

Typcially, γ might be around 1.4. Therefore, imagining a diesel engine with 17:1 compression, at starting temperature 298K (25°C) the resulting temp, T2, might be




Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.