Energy, Year 10: specific heat capacity and power

Specific heat capacity

HintThree words; the first one signals 'for each kilogram'.

The whyEvery material has its own value, in joules per kilogram per degree Celsius (J/kg °C). Water's is unusually high, about 4200 J/kg °C, which is why it takes so long to boil and makes a good coolant. The symbol is c.

84

HintThe equation has three quantities multiplied together; then look again at the unit asked for.

The whyChange in thermal energy = mass × specific heat capacity × temperature change = 2 × 4200 × 10 = 84 000 J, and 1000 J is 1 kJ. This equation is given on the AQA Physics equation sheet, so pupils need to select and use it, not memorise it.

900 J/kg °C

HintDivide the energy by the other two quantities multiplied together.

The whyRearranging ΔE = m c Δθ gives c = ΔE ÷ (m × Δθ) = 9000 ÷ (0.5 × 20) = 9000 ÷ 10. The unit follows from the working: joules divided by kilograms and by degrees Celsius.

The energy supplied, the mass of the block and its temperature rise

HintLook at what the equation needs on each side once c is the unknown.

The whyThe mass comes from a balance, the temperature rise from a thermometer read before and after, and the energy from a joulemeter (or from the heater's power multiplied by the time it is on). Then c = energy ÷ (mass × temperature rise). This is AQA required practical 14.

Some of the energy supplied heats the surroundings instead of the block

HintNot every joule counted by the meter ends up where you wanted it.

The whyThe calculation assumes all the measured energy went into the block. In fact some escapes to the air, the bench and the heater itself, so the block warms less than it should for that energy, and dividing by too small a temperature rise gives too large an answer. Insulation reduces the loss but cannot remove it.

Copper

HintA high value means each kilogram soaks up a lot of energy for every degree it gains.

The whyRearranged, the equation says temperature change = energy ÷ (mass × specific heat capacity). With the energy and mass equal, the material with the smaller specific heat capacity has the bigger temperature rise. That is why a metal pan heats up far faster than the water inside it.

Power

HintIt is the quantity printed in watts on a kettle or a light bulb.

The whyA powerful device is one that transfers a lot of energy every second, not one that holds a lot of energy. Its two equations, both to be recalled, are power = energy transferred ÷ time and power = work done ÷ time.

joule

HintIt is the standard unit for energy and for work done.

The whyThe watt is a compound unit: W = J/s. A 60 W lamp therefore transfers 60 of these units of energy every second it is switched on. Knowing this lets you check that a power calculation has its units right.

2000

HintShare the energy out equally between the seconds.

The whyPower = energy transferred ÷ time = 60 000 ÷ 30. AQA expects this equation to be recalled. The answer is a typical rating for a household kettle.

12 s

HintThe motor gets through 500 J every second; how many seconds until 6000 J are done?

The whyRearranging power = work done ÷ time gives time = work done ÷ power = 6000 ÷ 500. Both power equations must be recalled, and either can be rearranged for any of its three quantities.

They do the same work, but A has twice the power

HintOne of the two quantities depends only on the load and the height; the other also depends on the clock.

The whyWork done is force × distance, and both are identical, so the energy transferred is the same. Power is that work divided by the time taken, and A takes half the time, so its power is double. AQA names exactly this comparison as the example pupils should be able to give.

450 W

HintTwo steps: first the energy needed to raise her weight, then how quickly she supplied it.

The whyWork done = force × distance = 600 × 3 = 1800 J. Power = work done ÷ time = 1800 ÷ 4. The force is her weight and the distance is the vertical height, not the length of the staircase.