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.

Physics: pressure: how high a column of water might a household tap support?

The tutor imagines a water pressure scenario.

Let’s imagine the pressure of a faucet is 40psi (pounds per square inch). For the sake of physics, we might convert that pressure to N/m^2:


The gravitational force on a water column is density*area*height*9.8N/kg, all dimensions in metres:


Therefore, the force per unit area (ie, pressure) at the bottom of the column would be


At the maximum height the faucet can support, its pressure will equal that due to gravity:


Dividing both sides by 9800, we arrive at

28.18m = h

Therefore, a 40psi faucet should support a 28.18m column of water.

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

Thermodynamics: first law, with compression of a gas

The tutor begins about thermodynamics with the example of compressing a gas.

Thermodynamics is the analysis of energy – particularly, how it moves and/or changes form. The First Law of Thermodynamics is the Law of Conservation of Energy: Energy cannot be created or destroyed, but merely moves or changes form.

Let’s imagine a system that has internal energy U. Then U can change only by work or heat (Δ means change):

ΔU = q + w,

q= heat,

If q is negative, heat is leaving the system; if w is negative, the system is doing work against its environment.

The internal energy of an ideal gas is directly proportional to its temperature: specifically,

U = 1.5nRT, where

n= moles of gas present
R=8.315J/(K*mol), which is the gas constant
T=temperature in Kelvin

As a gas is compressed, work is done to it (so w is positive). Let’s imagine rapid compression that does not allow time for heat to escape, so q=0. Then according to

ΔU = q + w,

U must increase. Since

U = 1.5nRT

the temperature of the (ideal) gas must rise with compression.

The rise of temperature during compression enables diesel engines and refrigerators to work.


Giancoli, Douglas C. Physics, 5th ed. New Jersey: Prentice Hall, 1998.

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

Physical chemistry: efficiency of internal combustion engine in hot vs cold weather

The tutor examines the idea that internal combustion engines are more efficient in cold weather.

An upper limit for efficiency of an internal combustion engine is

eff = (Tcombust – Tsurrounding)/Tcombust


Tcombust is the temp of the combustion cylinder

Tcombust, Tsurrounding both in degrees Kelvin (Celsius + 273).

Let’s imagine a diesel engine, whose average internal cylinder temperature might be around 1600°C. Then at outdoor temp of 25°C (293K) we have

eff = (1873 – 298)/1873 = 84.1%

Likewise, at outdoor temp -25°C we have

eff = (1873 – 248)/1873 = 86.8%

The 2.7% increase in efficiency at -25°C vs 25°C may be noticeable to an operator.


White, J. Edmund. Physical Chemistry: College Outline Series. New York: Harcourt Brace Jovanovich, 1987.

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