4 Energy resources and energy transfers

Match the quantity before choosing the unit. Kilograms measure mass, whereas newtons measure force. Metres measure length, metres per second measure speed, and metres per second squared measure acceleration. Joules measure energy or work done, whereas watts measure power.

Example: as a dropped object falls, its gravitational store decreases and its kinetic store increases by mechanical transfer. When it stops on the floor, energy is transferred into thermal stores of the object and surroundings.

For any device or event, account for all the starting energy. Part may reach the intended useful store and the rest may be transferred into other stores, often thermal stores of the device and surroundings. The complete energy account is: total input energy = useful output energy + energy transferred to other stores.

Example: when a rough ramp raises a block, some input energy increases the block's gravitational store. Friction transfers the remainder into thermal stores of the block, ramp and surroundings. Adding those changes gives the original input energy.

Use energy values in the same unit. Identify the useful output from the purpose of the device, divide it by the total output, then multiply by 100%. To find total output instead, divide the useful output by the efficiency written as a decimal.

Example: 1800 J is transferred usefully at 16% efficiency. Write 16% as 0.16, so total output = 1800 J ÷ 0.16 = 11 250 J. The energy transferred to other stores is 11 250 J − 1800 J = 9450 J.

A Sankey diagram uses one input arrow that splits into labelled output arrows. Arrow width represents energy: the useful and other output widths must add to the input width. For a 25% efficient device, the useful arrow is one quarter of the input width and the other-output arrow is three quarters.

A metal spoon in hot water warms mainly by conduction. Water circulating in a heated pan transfers energy by convection. Energy from the Sun reaches Earth by radiation because space is a vacuum.

1. A region of fluid receives energy by heating. 2. Its particles move faster and spread farther apart, so the fluid expands and becomes less dense. 3. The warmer, less-dense fluid rises. 4. Cooler, denser fluid sinks or moves in to replace it. 5. Continued heating repeats the movement and forms a current.

A hotter object emits thermal radiation at a greater rate than the same object at a lower temperature. If an object emits energy faster than it absorbs energy from its surroundings, it cools; if it absorbs faster than it emits, it warms.

A black solar collector absorbs radiation effectively. A shiny silver surface on an insulated cup reduces both absorption and emission of infrared radiation, helping to limit transfer between the drink and its surroundings.

Keep dimensions, distance from the source, starting temperature, volume, heating time and heater output constant where relevant. Repeat each measurement, identify anomalies and compare means. Allow hot apparatus to cool before repeats and avoid contact with hot water or heaters.

The same mechanisms can keep a hot object hot or a cold object cold: they slow energy transfer across the temperature difference. A well-designed container combines features because blocking only one pathway leaves others available.

$W$ is work done in joules (J), $F$ is the force in newtons (N), and $d$ is the distance moved in the force direction in metres (m). Rearrangements are $F=W/d$ and $d=W/F$.

Example: a rope transfers 41 000 J of energy while pulling a truck 15 m in the rope's direction. $F=W/d=41\,000/15=2733\ldots$ N, so the force is $2.7\times10^3$ N to two significant figures.

Work describes the transfer process, not a separate energy store. Both work done and energy transferred are measured in joules because they are equal amounts in the same energy account.

$m$ is mass in kilograms (kg), $g$ is gravitational field strength in newtons per kilogram (N/kg), and $h$ is the vertical height change in metres (m). The energy change is in joules (J).

Example: a 14 g ball rises by 29 cm where $g=10$ N/kg. Convert first: $m=0.014$ kg and $h=0.29$ m. Then $\Delta\mathrm{GPE}=0.014\times10\times0.29=0.0406$ J, about $4.1\times10^{-2}$ J.

$m$ is mass in kilograms (kg), $v$ is speed in metres per second (m/s), and kinetic energy is measured in joules (J). To find speed, use $v=\sqrt{2\mathrm{KE}/m}$.

Example: a 0.014 kg ball has 0.051 J in its kinetic store. $v=\sqrt{(2\times0.051)/0.014}=\sqrt{7.29}=2.7$ m/s.

Example: a 0.0055 kg marble descends 0.21 m, so GPE lost is $0.0055\times10\times0.21=0.01155$ J. At 0.76 m/s its KE is $0.5\times0.0055\times0.76^2=0.00159$ J. The difference, about 0.010 J, has been transferred to other stores by friction and resistance.

One watt means one joule transferred each second: $1\,\mathrm{W}=1\,\mathrm{J/s}$. A 500 W device transfers 500 J each second while operating at that power.

Two people may do the same work climbing the same stairs. The person who completes the climb in less time has the greater power, even though both transfer the same amount of energy to their gravitational stores.

$P$ is power in watts (W), $W$ is work done and $E$ is energy transferred in joules (J), and $t$ is time in seconds (s). Rearrangements are $E=Pt$ and $t=E/P$.

Example: a heater transfers 39 kJ in 290 s. Convert $39$ kJ to $39\,000$ J, then $P=39\,000/290=134.5\ldots$ W, which is $1.3\times10^2$ W (130 W) to two significant figures.

In turbine systems, some energy is also transferred to thermal stores of the machinery and surroundings and by sound radiation. The resource changes the starting store or heating step; the turbine-generator stages are often shared.

A valid comparison matches the method to the need. Intermittent sources may require storage or support from controllable generation; reservoir hydro can release stored water when demand is high. Site suitability and environmental effects can rule out an otherwise useful resource.