Solved: A heater in an electric shower has a power of 8.5 kW when connected to a 240 V... [IB Physics (New syllabus)]

Question

SLPaper 2

A heater in an electric shower has a power of 8.5 kW when connected to a 240 V electrical supply. It is connected to the electrical supply by a copper cable. The following data are available:

Length of cable = 10 m

Cross-sectional area of cable = 6.0 mm²

Resistivity of copper = 1.7 × 10⁻⁸ Ω m

The heater changes the temperature of the water by 35 K. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹. Determine the rate at which water flows through the shower. State an appropriate unit for your answer.

[4]

Verified

Solution

recognition that power $=$ flow rate $\times c\Delta T$ 1 mark

flow rate $«=\frac{\text{power}}{c\Delta T} »=\frac{8.5 \times 10^{3}}{4200 \times 35}$ 1 mark

$=0.058 \ll \mathrm{kgs}^{-1} »$ 1 mark

$\mathrm{kg\ s}^{-1} / \mathrm{g\ s}^{-1} / \mathrm{l\ s}^{-1} / \mathrm{ml\ s}^{-1} / \mathrm{m}^{3} \mathrm{s}^{-1}$ 1 mark

Calculate the resistance of the cable.

[2]

Verified

Solution

$R=\frac{1.7 \times 10^{-8} \times 10}{6.0 \times 10^{-6}}$ 1 mark

$=0.028 «\Omega »$ 1 mark

Explain, in terms of electrons, what happens to the resistance of the cable as the temperature of the cable increases.

[3]

Verified

Solution

«as temperature increases» there is greater vibration of the metal atoms/lattice/lattice ions

**OR **

increased collisions of electrons 1 mark

drift velocity decreases «so current decreases» 1 mark

«as V constant so» $R$ increases 1 mark

Award [0] for suggestions that the speed of electrons increases so resistance decreases.

Calculate the current in the copper cable.

[1]

Verified

Solution

$I «=\frac{8.5 \times 10^{3}}{240} »=35$ A 1 mark

A heater in an electric shower has a power of 8.5 kW when connected to a 240 V electrical supply. It is connected to the electrical supply by a copper cable. The following data are available:

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