A student has two radiators in her home. They are filled with different liquids and have different power ratings. The diagram shows information about the two heaters. Oil radiator Water radiator 400 W heater 1000 W heater Specific heat capacity for oil = 1 680 J/kg°C Specific heat capacity for water = 4 200 J/kg°C (a) The radiators are turned on and both radiators increase in temperature by 40 °C in 1 680 seconds. Show, by calculation, that the heaters take the same time to heat up. (b) The student has two fires in her home (X and Y) shown in the diagrams below. X Y 1 kW output through chimney 4 kW output to room 5 kW input to fire 0.5 kW output through chimney Heat exchanger transfers energy to cold water in heating system. Why does fire Y help to save money on the energy bills for her home? Use calculations of efficiency in your answer.

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A student has two radiators in her home - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 4

Question 21

A student has two radiators in her home. They are filled with different liquids and have different power ratings. The diagram shows information about the two heater... show full transcript

Worked Solution & Example Answer:A student has two radiators in her home - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 4

Step 1

(a) Show, by calculation, that the heaters take the same time to heat up.

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Answer

To demonstrate that both heaters take the same time to heat up, we can use the formula for heat energy:

$Q = mc heta$

where:

$Q$ = heat energy (J)
$m$ = mass of the substance (kg)
$c$ = specific heat capacity (J/kg°C)
$heta$ = change in temperature (°C)

Calculate the heat energy required for the oil radiator:
- Mass, $m = 10$ kg
- Specific heat capacity, $c = 1,680$ J/kg°C
- Temperature change, $heta = 40$ °C
Substitute the values into the formula:

$Q_{oil} = 10 imes 1680 imes 40 = 672,000 ext{ J}$
Calculate the heat energy required for the water radiator:
- Mass, $m = 10$ kg
- Specific heat capacity, $c = 4,200$ J/kg°C
- Temperature change, $heta = 40$ °C
Substitute the values into the formula:

$Q_{water} = 10 imes 4200 imes 40 = 1,680,000 ext{ J}$
Determine the power and time taken by each heater:
- For the oil radiator:
  - Power = 400 W, so:
  $ext{Time}_{oil} = rac{Q_{oil}}{P} = rac{672,000}{400} = 1680 ext{ s}$
- For the water radiator:
  - Power = 1000 W, so:
  $ext{Time}_{water} = rac{Q_{water}}{P} = rac{1,680,000}{1000} = 1680 ext{ s}$

Both heaters take the same time of 1,680 seconds to heat up.

Step 2

(b) Why does fire Y help to save money on the energy bills for her home?

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Answer

To analyze the efficiency of the heating systems, we use the formula for efficiency:

$ext{Efficiency} = rac{ ext{Useful output energy}}{ ext{Input energy}} imes 100\\%$

Calculate the efficiency of fire X:
- Useful output = 4 kW (to room)
- Input = 5 kW
So, the efficiency of fire X is:

$ext{Efficiency}_X = rac{4 ext{ kW}}{5 ext{ kW}} imes 100\\% = 80\\%$
Calculate the efficiency of fire Y:
- Useful output = 4 kW (to room)
- Input = 5 kW - 0.5 kW (through chimney) = 4.5 kW
So, the efficiency of fire Y is:

$ext{Efficiency}_Y = rac{4 ext{ kW}}{4.5 ext{ kW}} imes 100\\% ext{ approximately } 88.89\\%$

Conclusion:
Fire Y has a higher efficiency (approximately 88.89%) compared to fire X (80%). This means fire Y provides more useful heat to the room with less energy loss, which helps to save money on energy bills.

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A student has two radiators in her home - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 4

Worked Solution & Example Answer:A student has two radiators in her home - OCR Gateway - GCSE Physics - Question 21 - 2021 - Paper 4

(a) Show, by calculation, that the heaters take the same time to heat up.

(b) Why does fire Y help to save money on the energy bills for her home?

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