Expert: Ahmed Salami - 1/8/2005

Question
Greetings Ahmed. I realise you may be very busy, but please do me a great favour by checking my answers here, as these are part of my major assignment! Please provide word equations to solve where I am wrong, and I can then do the rest myself.




A 1.53 kg mass of water is held in a well-insulated container. An electrical heating element with a constant power rating of 1kW is able to heat the contents of the container. Assume that all the energy from the element goies into heating the contents of the container and not the container itself.

a) What is the rate at which energy is transferred to the water from the heating element? Express your answer in J s^-1.
b) The water is initially at a temperature of 19 degrees Celsius. Assuming that the specific heat of water is 4.2 x 10^3 J kg^-1 degrees Celsius^-1, calculate how much energy is needed for the temperature of the water to reach 100 degrees Celsius.
c) Determine how long it will take for the water to reach a temperature of 100 degrees Celsius.
d) Calculate how long it takes to convert the water at 100 degrees Celsius into steam at 100 degrees Celsius, explaining any formula you use. (Assume the latent heat of vaporisation of water is 2.6 x 10^6 J kg^-1.)
e) If energy continues to be input into the container at the same rate, what will happen to the temperature of the contents after the water reaches 100 degrees Celsius? Explain in a few sentences.




My answers:

a) a) 1kw = 1000 J/s
b) E = (4.2x10^3)(100-19)(1.53) = 5.20x10^5 J
c) time = (1.53)(2.6x10^6)/1000 = 3.98 x 10^3 s

For part c), should the answer be the value above, or should it be this value instead?: "Since the heat needed to increase the temperature to 100oC is 5.2 x 10^5 Joules and since the heater is adding energy at the rate of 1000 Joules per second, dividing the heat needed by the rate at which heat is being added will give the time. time = 5.2 x 10^5J/1.0^3J/s = 520 seconds. [Note that the units are J/J/s = s!]"
 
What are your suggestions for parts d) and e)?  

Answer
Hi Mafkhir,
Please forgive the delay. I was on vacation.
The answers to a and b are correct.
The second answer to c is the correct one.
The energy required for d) is
ml where l is the latent heat . So the incorrect answer in c) is the correct answer for d).
As for e), the temperature remains at 100 degrees while all the water changes into steam.
Please let me know how you fare with this.
Good luck.
Regards.