Lecture 6 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 Power = Work done Time taken to do the work P W t Work is measured in Joules, time in seconds SI unit of power is the Watt 1Watt 1J 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 = 0km/h V = 100km/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, P W t P Ferrari = (396,000J/5s) = 79.2kWatts P old 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) Power = Work done Time taken P W 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 Eff work 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 W out results in an equivalent energy (E out ), we can also write: energy Eff energy out energy And since power is rate of doing work or of transferring energy, we can also write: Powerout Eff Power in in out in
Example Efficiency 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? Eff energy energy out in E out = E in * Eff = 100,000J*0.9 = 90kJ P W t t W P Time (t) = W/P = (90kJ/100W) = 900 seconds t = 15min
Other energy units Power = Work done Time taken to do the work Power is the also rate at which energy is used P W t E 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 1.33 Watts. How much energy is produced by the heart in a day. P E E Pt t E 1.33 watts (60 60 24)sec onds E 1.15 10 5 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: 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 Main sources Fat, Protein, Carbohydrates and Alcohol Energy content (kcal/kg) Fat 9.3x10 3 Butter 7.2x10 3 Alcohol 7.0x10 3 Protein 4.1x10 3 Carbohydrate 4.1x10 3 Sugar: 4.0x10 3 Carrots: 0.42x10 3 Celery* 0.14x10 3
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 O 2 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
Energy required for: Human energy 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 Food energy in mammals is shared between 3 functions: (i) doing work (ii) keeping warm (iii) storage Consumption rate: some activities Activity Sleeping 1.2 Sitting at rest 1.7 Standing relaxed 1.8 Sitting in class 3.0 Walking slowly (4.8km/hr) rate (kcal/min) 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 Eff work out energy in Eff P out P in Human efficiency depends on cooperative use of muscles to produce work and energy used by other organs Maximum efficiency 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 Eff work out energy in Energy in = work out /eff = (1911)/0.20 = 9555J 4186 J = 1kcal Energy in = 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 KE i +PE i +OE i = KE f +PE f +OE f 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
Example Human energy 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 Time = energy 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.
Exercise: Mountain Climber 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: E consumed = 9.8 * (time) kcal E consumed = 9.8*3*60 kcal = 1764kcal Convert to Joules E consumed = 1764 * 4186 J = 7384kJ Efficiency Eff = PE/E consumed = 735/7384 10.0%