Leaving Cert Physics Heat & Heat Transfer: The diagram shows a water boiler

The diagram shows a water boiler which is filled with 0.7 kg of water which is initially at 20 °C - Leaving Cert Physics - Question (c) - 2018

Question (c)

The diagram shows a water boiler which is filled with 0.7 kg of water which is initially at 20 °C. The boiler has a power rating of 3 kW. (i) Calculate the energy ... show full transcript

Worked Solution & Example Answer:The diagram shows a water boiler which is filled with 0.7 kg of water which is initially at 20 °C - Leaving Cert Physics - Question (c) - 2018

Step 1

Calculate the energy needed to raise the temperature of the water from 20 °C to 90 °C.

96%

114 rated

Answer

To find the energy needed, we can use the formula:
$E = mc heta$
where:

$m = 0.7 \, kg$ (mass of water)
$c = 4200 \, J \, kg^{-1} \, °C^{-1}$ (specific heat capacity of water)
$heta = (90 - 20) = 70 \, °C$ .
Substituting the values we have:
$E = 0.7 imes 4200 imes 70$
Calculating this gives:
$E = 205800 \, J$

Step 2

How many joules of energy are supplied per second by the boiler?

99%

104 rated

Answer

The power of the boiler is given as 3 kW, which can be converted to joules per second.
1 kW = 1000 J/s, so:
$3 \, kW = 3000 \, J/s$
Therefore, the boiler supplies 3000 joules of energy per second.

Step 3

Calculate how long it will take the boiler to heat the water to 90 °C.

96%

101 rated

Answer

To find the time needed to heat the water, we use the formula:
$E = Pt$
where:

$E = 205800 \, J$ (energy calculated earlier)
$P = 3000 \, J/s$ (power of boiler)
Rearranging gives us:
$t = \frac{E}{P} = \frac{205800}{3000} \approx 68.6 \, seconds$

Step 4

Where should the manufacturer place the heating element of the boiler? Explain your answer.

98%

120 rated

Answer

The manufacturer should place the heating element at the bottom of the boiler.
This is because hot water is less dense than cold water, so it rises to the top.
By placing the heating element at the bottom, it ensures that the cold water will be heated effectively, facilitating better energy transfer and quicker heating of the entire water volume.

The diagram shows a water boiler which is filled with 0.7 kg of water which is initially at 20 °C - Leaving Cert Physics - Question (c) - 2018

Worked Solution & Example Answer:The diagram shows a water boiler which is filled with 0.7 kg of water which is initially at 20 °C - Leaving Cert Physics - Question (c) - 2018

Calculate the energy needed to raise the temperature of the water from 20 °C to 90 °C.

How many joules of energy are supplied per second by the boiler?

Calculate how long it will take the boiler to heat the water to 90 °C.

Where should the manufacturer place the heating element of the boiler? Explain your answer.

Join the Leaving Cert students using SimpleStudy...