An aluminium kettle of mass 2kg holds 2.00×10^3cm of water and consume electric power at the rate of 2kw. If 60% of the heat supplied is wasted, find the time taken to bring the kettle of water to boiling point from an initial temperature of 25°c.(specific heat capacity of water and aluminiun are 4.18 and 0.84j/g-1 °c)
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To find the time taken to bring the kettle of water to boiling point, we need to calculate the amount of heat required to raise the temperature of water from 25°C to its boiling point and then calculate the time using the power consumed by the kettle.
Step 1: Calculate the heat required to raise the temperature of water from 25°C to boiling point.
The heat formula is given by:
Q = m * c * ΔT
Where:
Q is the heat energy
m is the mass of the water
c is the specific heat capacity of water
ΔT is the change in temperature
Given:
Mass of water (m) = 2.00×10^3g
Specific heat capacity of water (c) = 4.18J/g-1°C
Change in temperature (ΔT) = Boiling point (100°C) - Initial temperature (25°C) = 75°C
Substituting the values into the formula:
Q = (2.00×10^3g) * (4.18J/g-1°C) * (75°C)
Step 2: Calculate the total heat supplied by the kettle.
Since 60% of the heat supplied is wasted, we need to find the total heat supplied:
Total heat = 100% heat required / (100% - 60%)
= Q / 0.4
Step 3: Calculate the time taken.
The power formula is given by:
P = W / t
Where:
P is the power consumed (2kW)
W is the total heat supplied
t is the time taken
Substituting the values into the formula:
2kW = (Total heat supplied) / t
Simplifying:
Total heat supplied = 2kW * t
Now, equating the total heat supplied to Q/0.4:
2kW * t = Q / 0.4
Solving for t:
t = (Q / 0.4) / 2kW
Now you can substitute the calculated values for Q and solve for t.