An electric water heater contains a tube through which water flows at a constant rate.

Question 8

(a) Two metal spheres are in thermal equilibrium.

State and explain what is meant by thermal equilibrium. [2]

(b) An electric water heater contains a tube through which water flows at a constant rate.

The water in the tube passes over a heating coil, as shown in Fig. 3.1.

Fig. 3.1

The water flows into the tube at a temperature of 18 °C. When the power of the heater is

3.8 kW, the temperature of the water at the outlet is 42 °C.

The specific heat capacity of water is 4.2 J g^-1 K^-1.

(i) Use the data to calculate the flow rate, in g s^-1, of water through the tube. [3]

(ii) State and explain whether your answer in (i) is likely to be an overestimate or an

underestimate of the flow rate. [2]

Reference: Past Exam Paper – November 2012 Paper 41 & 42 Q3

Solution:

(a) Two metal spheres are said to be in thermal equilibrium when the temperatures of the two spheres are the same and there is no (net) transfer of energy between the spheres.

(b)

(i)

{Heat energy = mcΔθ

Power = energy / time = mcΔθ / t = (m/t) cΔθ

The quantity m/t is the flow rate of water through the tube. That is, the mass of water flowing per second.

Unit of m/t = [mass] / [time] = g s^-1    when mass is given in gram}

Power = (m/t) cΔθ

3800 = (m/t) × 4.2 × (42 – 18)

Note: no need to convert tempt to Kelvin here, because the difference would be the same value

m/t = 38 g s^-1  

(ii) Some thermal energy is lost to the surroundings. So the rate is an overestimate.

{Some of the energy is lost and therefore, not used to heat the water.

Power = energy / time. So, the value of power gives us how much energy is provided per time.

Power = (m/t) cΔθ                   So, (m/t) = Power / cΔθ

In the above calculation, we have taken the power to be 3800 W. But we know that some energy is lost to the surroundings and is not used for heating the water. So, the actual value that should be used must be less than 3800 W.

 
BUT since we have taken the power as 3800 W, the value of m/t obtained is greater than it really should. So, the value obtained is an overestimate.}