[1] A kilowatt-hour (kW⋅h / kW h; or kWh) is an energy non-SI unit equal to 3.6 megajoules (MJ) in SI units, the energy delivered by a kilowatt of power for 1 hour. kWh is a common electrical billing unit energy supplied by electric utilities.
Metric prefixes are used for many and submultiples of the unit, the watt-hour (3.6 kJ).
a rating label
To know energy requirements and costs power a device, all devices have a label (rating label) at the back saying watts it uses. These contributes the bill's total sum.
Estimating the total power requirements for all unit help identify which appliances use the most energy.
To estimate the household energy usage, have:
electric bills
equipment ratings
expected load profiles
List all devices' wattages.
Estimate average daily use (hours per day).
Multiply wattage by hours used to get watt-hours.
Convert watt-hours to kilowatt-hours by dividing by 1000.
Calculate monthly usage by multiplying daily kWh by the number of days in a month.
Estimate costs by multiplying monthly kWh by the cost per kWh from your electric bill.
The output is electrical power--what motors use from a power source.
The input is mechanical power--what a motor sends to turn on shafts/drive cars/etc.
To tell which is the output, which the input E.g. A 10 HP rated motor connects to a 220 V power supply. The motor draws a 25 A.
Here, the output is 10 HP = 10x746 = 7460 W is the output as it's power the motors sent to the load.
220x25 is the input as it's power drawn from the electric supply
[1]
4# A pc of 87% efficient uses 375 kWh energy.
How much useful energy does it give?
POUT = 1.3 * 746 = 969.8 W
PIN = 120 * 20 = 2.4 kW
ɳ = 969.8/2400 * 100% = 40.41%
How much power is wasted?
Plosses = 2400 - 969.8 = 1430.2 W
[1] Electrical efficiency is the amount of useful energy to a motor--how much left after heat loss, divided by PT consumed (a fractional expression), often denoted by Greek letter Eta η.
Power output formula (Pout): torque × angular speed (Tω) or if in horsepower (hp) as 1 hp = 746 W:
torque (T): twisting force used (in Newton-meters, N·m).
angular speed (ω): speed a shaft rotates (in radians per second; rad/s).
Power input formula (Pin): voltage x current (IE; Ohm's law)
Wasted power formula: (Ploss): Pin - Pout
Efficiency formula: ɳ = (𝑃𝑜𝑢𝑡/𝑃𝑖𝑛) x 100%
ɳ = % efficiency
Overall efficiency formula: ɳr = ɳ1 x ɳ2 x ɳ3
𝜂𝑟 = overall efficiency
Some losses always occur, so efficiency is always under one. As some machines have great efficiency (e.g. transformers which can be at 98%) others like electronic amplifiers maybe low as 50%.
1# If a 120 V DC motor draws 20 A and develops a 1.3 hp (horsepower) output power, what's the efficiency?
Note: 1 hp (horsepower) = 746 W
POUT = 1.3 * 746 = 969.8 W
PIN = 120 * 20 = 2.4 kW
ɳ = (969.8/2400)100% = 40.41%
How much power is wasted?
Plosses = 2400 - 969.8 = 1430.2 W
2# A 2.5 HP motor connects to a 240 V DC and draws 10 A.
What's the efficiency?
POUT = 2.5 * 746 = 1.865 kW
PIN = 240 * 10 = 2.4 kW
ɳ = 1.865/2.4 * 100%
ɳ = 77.71 %
How much power is wasted?
PLOSSES = 2400 – 1865 = 535 W
3# With a system of many cascaded motors, how do we calculate total efficiency?
Calculate all individual efficiencies and multiply for the answer.
ɳr = ɳ1 x ɳ2 x ɳ3
If we have with this system:
Motor 1 ɳ1 = 92%
Motor 2 ɳ2 = 84%
Motor 3 ɳ3 = 88%
, efficiency is:
= 0.92 x 0.84 x 0.88 = 68%
power out is a combination of "power in" and "power losses": → Pout = Pin – Plosses
How much kilowatts a device uses is found with its power rating.
E.g. a 60 W light bulb uses 60 Watts--After being on for 18h, it used 60x18=1080 W = 1.08 kWh
1# How much kWhs a 750 W air conditioner uses over a 24 h space if always running?
Reveal answer750W x 24h = 18000 watt-hours/18 kWh
2# How much kWhs a dryer uses if rated 15 A and plugged into 240 V, for 45 m?
Reveal answer45 m = 45/600 = 0.75 h
15A x 240V x 75h = 2700 watt-hours/2.7 kWh
With answers in 2#, if the rate is 11 ¢/kWh, how much will the devices cost, each and in total?
Reveal answer18 x 0.11 = $ 1.98 → air conditioner
2.7 x 0.11 = $0.30 → dryer
1.98 + 0.30 = $2.28
Total cost: 1.98 + 0.30 = $2.28
If a household uses 750 kWhs per month, the average cost a month at 11 ¢/kWh is:
Reveal answer750 x 0.11 = $82.50
If a 40 W light bulb stays on for 30 days, the cost per kWhr is $0.28. How much will it cost?
Reveal answer40 W * 24 hr * 30 day = 28.8 kWh
28.8 x 0.28 = $8.06
What's the cost per month of a household using 875 kWhs a month with a 14 ¢/hr electricity rate?
Reveal answer875 x 0.14 = $122.50
If a 60 W bulb is left on for 30 days, the cost is 15 ¢/kWh:
60 W x 30 days * 24 hr = 43.2 kWh
43.2 x 0.15 = $6.48
The law of energy conservation says energy is neither created nor destroyed. But we can convert it to another energy type.
Electrical energy is converted into mechanical energy to run motors.
As some energy is converted to heat, although no energy is lost, not all of is available to be used by the motor
[Q4] There are 4 key ways to measure energy--are transformations and losses across a energy chain: Primary, secondary, final, and useful energy.
Note: 1st stage (‘primary energy’) and last (‘useful energy’)'s differences are wide--be sure to be clear to refer which metric if we talk for data on “energy”.
Primary energy is the energy is available as resources (e.g. fuels burnt in power plants (E.g. before it's transformed; coal before burning; uranium; or barrels of oil).
Secondary energy: If we convert primary energy into a transportable form we speak of secondary energy. E.g. Burned coal in a power plant that make electricity is secondary energy; liquid fuels (e.g. gasoline and diesel, which are refined oil), electricity, and heat).
Final energy is what we buy and receive (E.g. home electricity; heating; petrol at fuel pump).
Useful energy is transferred energy to use. E.g. For a lightbulb, it’s how much light is made. In a car, it’s how much kinetic energy is made.
Useful energy equation = effiency percentage x energy used
Not energy used (especially for use) is waste.
E.g. Lightbulb's useful energy is light, but heat is also made. Cars's useful energy is is movement, but they also make heat and noise.
Primary to secondary energy: conversion of primary to secondary energy is inefficient. In thermal power plants (convert fossil fuels, biomass or nuclear into electricity) 2/3 of primary energy is wasted as heat. Each 3 energy units, we get 1 electricity unit out.
Note: As primary energy losses are big for fossil fuels, their contribution to energy demand is higher than other measuring energy ways--crucial to know as it can skew perception of how much a contribution low-carbon sources make: in primary energ, they seem smaller due being diluted by wasted energy coming with fossil fuel burning.
Secondary to final energy: we also lose energy in the process of delivering it to the consumer. This is called a ‘transmission and distribution’ loss. When we transport electricity from a power plant (secondary energy) to homes (final energy), for example, we lose some while transmitting it through power lines.
Final to useful energy: no appliance is completely efficient in providing only the desired output that we want.
[Q1] Flashcards
[Q2] Exercises - Canva
[Q3] Exercises - Ms. Simpson's class site
[QA3] Exercises (answers)
[Q4]