Lecture 6
Energy
Power
Efficiency
Food Energy
Power
Power is the amount of work done per unit time
Power is the also rate at which energy is used
Work done
Power = Time taken to do the work
W
P
t
Work is measured in Joules,
time in seconds
SI unit of power is the Watt
1J
1Watt 
1s
James Watt 1736---1819
Scottish engineer and inventor
Power
For machines the common unit of
power was called horsepower.
1horsepower  746Watts
33,000 foot-pounds per minute
Horse
Power
Example:
V = 100km/h
V = 0km/h
W = 396kJ
Ferrari: in 5 sec
Old car: in 30 sec
Calculate power required in each case
The same work is done by the two cars,
W
P
t
PFerrari = (396,000J/5s) = 79.2kWatts
Pold car = (396,000J/30s) = 13.2kWatts
power is much greater in the first case:
Example
Calculate the power expended by a person of
mass 65kg in climbing a flight of stairs 3m high,
(a) in 10 seconds (b) in 3 seconds
Work done = mgh
(increases gravitational potential energy)
W= {65kg*9.8ms-2*3m}= 1911.0J
(a)
Work done
Power = Time taken
W
P
t
P = 1911.0J/t = 1911.0J/10s
= 191.1(J/s) = 191.1Watts
(b)
Work done is the same, 1911Joules
but in a shorter time
Power = (1911.0J)/t = (1911.0J)/3s = 637 Watts
Efficiency
Some energy is always “wasted”
when work is done
Energy goes into form that is not wanted
Incandescent Light bulbs for example :
Much of electrical energy they consume
goes into thermal energy rather than light
Similar for cars: some of the energy
consummed is converted to thermal energy
Also “wasted” food energy in humans and
animals goes mostly into thermal energy
This leads us to the concept of efficiency
Efficiency
Efficiency is the ratio of useful work
output to the energy input
workout
Eff 
energyin
It has no unit, and is often given in %.
The efficiency is never 100%, because in
reality, part of the input energy is dissipated
(by friction for example) and is transferred into
thermal energy
Since Wout results in an equivalent
energy (Eout), we can also write:
Eff = Eout /Ein
And since power is rate of doing work or of
transferring energy, we can also write:
Eff = Pout /Pin
Efficiency
Example
A battery has 100kJ of energy stored. If it is
90% efficient in giving up energy, how long
can it run a 100W light bulb?
workout
Eff 
energyin
Wout = Ein * Eff = 100,000J*0.9 = 90kJ
W
P
t
W
t
P
Time (t) = W/P = (90kJ/100W)
= 900 seconds
t = 15min
Other energy units
Work done
Power =
Time taken to do the work
Power is the also rate at which energy is used
W E
P 
t
t
E  Pt
(1) Energy is often expressed in units of
power x time:
e.g. electrical energy kilowatt-hour (kWh):
1kWh = 1000W*3600seconds
1kWh = 3600kJ = 3.6MJ
Example
The average power output of a beating heart
is 1.33watts.How much energy is produced by
the heart in a day.
E
P
t
E  Pt
E  1.33watts  (60  60  24)sec onds
E  1.15 105 Joules
Food Energy
The only energy that our bodies can utilise
is the chemical binding energy of the
molecules in our food.
Plants: Radiation from Sun → photosynthesis
Energy which supports us is locked into the
molecular bonds of a few basic fuel molecules:
glucose, fructose, fatty acids, and amino acids.
The energy is released as the energy-supplying
molecules are dismantled by oxidation.
Food Energy
Chemically stored energy:
foods and other fuels.
Energy contents of foods given in
units of kilocalories. 1kcal = 4186J
Fat, Protein & carbohydrates—main sources
Energy content (kcal/kg)
Fat
9.3x103
Butter
7.2x103
Alcohol
7.0x103
Protein
4.1x103
Carbohydrate
4.1x103
Sugar:
4.0x103
Carrots:
0.42x103
0.14x103
Celery*
Food Energy
For food and fuels the essential process by
which stored chemical energy is realised is
Oxidation (oxygen consumed)
4.83kcal of energy produced
per litre of O2 consumed
Body has no method of eliminating
excess caloric intake
If a human or animal consumes more food than
is required to do work or keep warm the excess
energy is stored in additional fatty tissue
If caloric intake is less than demand
body consumes its own tissue
Human energy
Energy required for:
•Physical work
•Blood circulation
•digestion
•Sleeping
•Brain activity (thinking)
Body converts stored chemical energy (food)
into
Mechanical work
Thermal energy
Stored chemical energy (fat)
Conversion rate → metabolic rate
Total energy conversion rate of a person at
rest is called basal metabolic rate (BMR)
BMR depends on personal characteristics
Average ≈ 70 kcal/hr
Human energy
Exercise:
important for weight control
Burning off calories
Also
increases body’s metabolic rate
Increased rate continues after exercise
Metabolic rate is proportional to
rate of Oxygen consumption
Human energy consumption rates
Consumption rate: some activities
Food energy in
mammals is
shared between
3 functions:
(i) doing work
(ii) keeping warm
(iii) storage
Celery*
14 kcal/100g
Chewing
digesting
Activity
rate (kcal/min)
Sleeping
1.2
Sitting at rest
1.7
Standing relaxed
1.8
Sitting in class
3.0
Walking slowly
(4.8km/hr)
3.8
Cycling (15km/hr)
5.7
Playing tennis
6.3
Swimming
6.8
Ice skating (15km/hr)
7.8
Climbing stairs
(116/min)
9.8
Playing basketball
11.4
Cycling
(professional)
26.5
Adapted from J.Cameron &J. Skofronick, Medical Physics
(Wiley Interscience, New York 1978.
The energy consumption increases strongly
with effort →(Oxygen consumption)
Human efficiency
workout
Eff 
energyin
Pout
Eff 
Pin
Human efficiency depends on
cooperative use of muscles to produce work
and energy used by other organs
Maximum 25%
*Example
A person of mass 65kg climbs a flight of stairs
3m high. How much food energy in kcal does
the person require if their body is 20% efficient.
Work done = mgh
(increases gravitational potential energy)
w= {65kg*9.8ms-2*3m}= 1911.0Joules
workout
Eff 
energyin
Energyin = workout/eff
= (1911)/0.20 = 9555J
4186 J = 1kcal
Energyin = 9555/4186 kcal = 2.3 kcal
*Example
A person of mass 65kg climbs a flight of stairs
3m high in 10 seconds. What is his rate of
thermal energy production in watts?
“wasted” food energy in humans and
animals goes mostly into thermal energy
KEi +PEi+OEi = KEf +PEf+OEf
0 + 0 + food energy =0 + mgh + thermal energy
Thermal energy = food energy – mgh
previous example, energy required if body is 20% efficient
Thermal energy = *9555J – (65* 9.8* 3)J
Thermal energy = (9555 – 1911) J =7644 J
Power = Rate of thermal energy production
P = (thermal energy)/(time)
(7644 J) / 10 s = 764.4 Watts
Human energy
Example
Calculate the energy in kilocalories needed
to play tennis for 2hours? What fraction of this
energy would be supplied by a soft drink
containing 50g of sugar?
Playing tennis uses 6.3kcal/min.
So for 2h: E = 6.3*120 kcal = 756kcal
Sugar has a caloric content of 4.0kcal/g.
Thus 50g of sugar have: 50*4.0kcal =
200kcal.
The fraction of the energy supplied by the
sugar is:
200/756 = 26%
Example
A person normally needs 3000 kcal of food
energy per day but instead consumes
4000 kcal. The energy consumption rate for
cycling is 10 kcal per minute.For how long
should he cycle to work off the excess
food energy intake?
Excess food energy intake =1000 kcal
energy
Time = energy/time =
1000 kcal
10 kcal/minute
Time = 100 minutes
Example
How many grams of fat will an inactive
person gain in a week if he consumes
2500Kcal of food per day? Power
consummed at rest is 1.22 kcal per minute and
1gram of fat is equivelent to 9.3 kcal.
His energy requirement:
for 1 minute is 1.22kcal
for 1 week is 1.22kcal *60*24*7 =12,297.6kcal
His intake is 2500kcal per day
or 2500*7 = 17,500 kcal per week
His excess food energy per week is:
(17,500 – 12,297.6)kcal = 5202.4kcal
1gram of fat is equivelent to 9.3 kcal
His mass gain in a week is
5202.4kcal *(1.0 g fat/9.3kcal) = 559.4 g of fat.
Mountain Climber
Exercise:
A 75kg man climbs a mountain 1000m high in
3.0h and uses 9.8kcal/min. What was the
efficiency of this man during the climb?
Change in potential energy: PE = mgh
PE = (75 * 9.8 * 1000) J = 735kJ
Total energy consumed:
Econsumed = 9.8 * (time) kcal
Econsumed = 9.8*3*60 kcal = 1764kcal
Convert to Joules
Econsumed = 1764 * 4186 J = 7384kJ
Efficiency Eff = PE/Econsumed = 735/7384 ≈ 10.0%