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Homework Statement
Hey physicists. I have a problem. My assignment this term for physics is to test the efficiency of an electrical appliance, and to make suggestions on how to improve the efficiency for the future.
I conducted a number of experiments on the kettle, using 2 different kettles. Each kettle was tested 3 times for each volume of water, each testing 500mL, 1,000mL and 1,500mL volumes.
After all the data was recorded - Temperature before boil, time taken to boil, temp. after boil - I was able to work out the energy absorbed by the water, the average power taken to heat the water over the duration, and finally the efficiency.
From the data, the efficiencies of all three experiments per volume of water were averaged out, giving for kettle a:
500mL - 80%
1,000mL - 86%
1,500mL - 92%
This shows a 6% increase in efficiency per 500mL increase in volume. I graphed this to show the linear relationship, and then it came to explaining this... And I am stumped.
I have searched the internet for hours and hours on end, and have not been able to determine the reason for this increase in efficiency. PLEASE help me find out why? My teacher told me he can't tell me the reason, i have to find it myself.
He said two things will help me. The shape of the kettle, and the surface of the water compared to the volume.
From this I developed only 1 reason... The surface of the water was being reduced as more water was added in, due to the shape of the kettle (reducing in size as it got closer to the top of the kettle, thus the more water, the less surface area). This would explain that water heated by conduction between water and the element on the bottom of the kettle, which then became less dense and was displaced upwards by the more dense water; creating a convectional current. The heat lost would slowly decrease as more water was added due to the shape as there is a smaller surface area.
But the second kettle remained the same in shape from base to top. So this cannot be the full reason?
Homework Equations
The equations I used were viewed by my teacher and he told me they were fine, but I will show them anyway.
For Test 1, 500mL Kettle A:
Temp before boil: 19°
Time taken (secs): 97s
Temp after boil: 98°
This allowed me to determine the heat absorbed by the water using Q = m.c. Δt where m is mass of water, c is specific heat capacity of water, and Δt is the change in temp.
Q = 500 x 4.186 x (98-19)
Q = 2093 x (79)
Q = 165,347 J
This shows 165,347 J was absorbed by the water.
From this, we could find the average power to run the kettle with P = E/T where E is the energy absorbed and T is the time in sec.
P = E/T
P = 165,347/97
P= 1704.608247
∴ P ≈1705W
Finally the efficiency was determined using E = (Pout/Pin)x100% where Pout is the power output (1705W) and Pin is the power input (found on the kettle, 2100W).
E = (1705/2100)x 100
E = 0.8119047619 x 100
E ≈ 81%
The Attempt at a Solution
As stated earlier:
"I developed only 1 reason... The surface of the water was being reduced as more water was added in, due to the shape of the kettle (reducing in size as it got closer to the top of the kettle, thus the more water, the less surface area). This would explain that water heated by conduction between water and the element on the bottom of the kettle, which then became less dense and was displaced upwards by the more dense water; creating a convectional current. The heat lost would slowly decrease as more water was added due to the shape as there is a smaller surface area.
But the second kettle remained the same in shape from base to top. So this cannot be the full reason? This is the only reason I can think of that would explain the efficiency of an electric kettle increasing as more water is added. The surface area in the kettle that changes shape, decreases the surface area of the water, and this reduces the availability of heat to escape through the water.
What other reasons could do this, and what could increase the efficiency of a kettle?
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