Power and Efficiency. Energy

Transcription

1 Power and Efficiency Foundation Physics Lecture Jan 10 Energy Energy is defined as the ability to do work. Work done by a system takes energy out of it, and conversely work done on a system puts energy into it. ΔE=W W: work done on a body. The additional energy enables the body to do work. Energy is stored work Kinetic and potential energy are the two main forms of energy.

2 Energies in the small world Boltzmann s constant: ~the amount of thermal energy per molecule per degree k = 1.38 x J/K (sometimes k B ) kt = 4.1 x J ~ 4 pn nm (at 25 o C) Covalent bond: ~600 pn nm = 150 kt Hydrogen bond: ~30 pn nm = 7.5 kt Photon (green, λ=500 nm): ~400 pn nm = 100 kt Hydrolysis of one ATP: ~80 pn nm = 20 kt Folding energy for a protein: ~100 pn nm = 25 kt The ribosome 1 ev = 160 pn nm = 40 kt (or kt ~ 25 mev) Kinetic and potential energy Energy of motion 1 2 m v 2 Linear kinetic energy 1 2 J ω 2 Rotational kinetic energy Energy of the position r 2 m g h 1 D x 2 Potential Energy Potential Energy in a spring

3 Example: Conservation of Energy Conservation of total energy Energy is transferred from system A to system B when the box is lifted. Neither system is closed. A larger single system containing both the person and the box is closed. Energy is transferred between components inside the system, none enters or leaves the system.

4 Conservation of total energy Energy can not be generated nor can it be destroyed. Energy only can be converted from one form into an other E tot = E pot + E kin = const. The energy of a system remains always constant: Changes in energy can only be explained with a gain or loss of energy in the system in form of heat or radiation. Energy conversion Lets consider the kinetic and the potential energy of a mass in the gravitational field of the earth. The weight is given by: F = m. g From the definition of the potential energy: de pot = -F x.dx dx de F = { x { dt dt mv& x d dt v x de dt kin + ( E + E ) = 0 kin de pot dt pot pot = mv& = 0 x v x = de dt kin E kin + E pot = const. Energy law for the kinetic and the potential energy for conserved forces (without friction)

5 Free fall from height h What is the speed v I immediately before impact? Applying the energy conservation law we observe two states 1 and 2: E 1 = E 2 E kin1 +E pot1 =E kin2 +E pot2 0+m. g. h 0 =1/2 mv I2 +0 v I = 2 gh 0 Power Power: the time rate of doing work P = dw / dt (1J/s=1W) The Si unit for power is the joule per second, which is called the watt (W) after James Watt ( ) 1 horse power = 746W From the power unit W often the energy unit W. h (watt hours) is derived: 1kWh = 3.6 x 10 6 J

6 Problems Calculate the amount of power used by an elevator 1200-kg traveling with a speed of 5 m/s upwards.. Orders of magnitude of power Nerve cells Human Train engine Saturn rocket Nuclear power plant Sun Supernova 10-9 W 10 2 W W 10 8 W W W W

7 Problems What is the average power consumption in watts of an appliance that uses 0.75 kwh of energy in one day? Problems To what form is most energy expended by a swimmer ultimately when she swims at a constant velocity?

8 Efficiency Efficiency is a measure of how much USEFUL energy you get out of an object from the energy you put INTO it. For example, consider a TV: Electrical Energy (200J) Sound (40J) Efficiency = Useful energy out Energy in x100% Efficiency The more efficient a device is the more work it will do with a given energy input. Efficiency is defined as: Eff = W out / E in Eff = E out / E in Eff = P out / P in Where W out is the useful work produced by the device and E in is the energy input

9 Efficiency Efficiency (%) of the body and of mechanical devices Body Cycling 20 Swimming, surface 2 Swimming, submerged 4 Shoveling 3 Steam engine 17 Gasoline engine 38 Nuclear power Plant 35 Coal power plant 42 Work, energy, power and efficiency in humans Basal Metabolic Rate and Oxygen Consumption Rate ORGAN Power Consumed % of BMR at Rest kcal/min (W) Liver and spleen Brain Skeletal muscle Kidney Heart Other Totals BMR: Total energy conversion rate of a person at rest, basal metabolic rate

10 Anaerobic and Aerobic Phases Humans and other animals are capable of doing work for short periods of time at much higher rates than can be maintained for long periods of time. To do this, the body rapidly oxidizes available blood sugar with oxygen already present in the body and makes the resultant energy available to vital organs and skeletal muscles. This stage is called the anaerobic phase because no ingestion of oxygen is required. Problems It is reasonable to assume that the body obtains as much energy from breaking down its own fatty tissue as it does from digesting fat. How many grams of fat will be lost by a person who swims 2.0 hr, sleeps 8.0 hr, and sits at rest the remainder of the day, if he consumes 2000kcal? Swimming breaststroke Sleeping Sitting at rest Fat 6.8 kcal/min 1.2 kcal/min 1.7 kcal/min 9.3 kcal/g

11 Next Lecture To Be Covered: Temperature and heat Reading: Chapter 5 Section 5.1 Section 5.2