An electric kettle used to prepare tea, takes 2 minutes to boil 4 cups of water (1 cup contains 200 cc of water) if the room temperature is 25°C.
(a) If the cost of power consumption is Rs. 1.00 per unit (1 unit = 1000 watt-hour), calculate the cost of boiling 4 cups of water.
(b) What will be the corresponding cost if the room temperature drops to 5°C?
Given-
Time taken to boil 4 cups of water, t = 2 minutes
Volume of water boiled = 4 × 200 cc = 800 cc
Initial temperature, θ1 = 25°C
Final temperature, θ2 = 100°C
Change in temperature, θ = θ2 − θ1 = 75°C
Mass of water required to boil , m = 800 × 1 = 800 gm = 0.8 Kg
Now heat required for boiling water,
Where
m is the mass of the water
s is the specific heat of the water
θ is the change in temperature
Putting the value in the above formula, we get
We know, to convert watt-hour to watt-sec,
1000 watt – hour = 1000 × 3600 watt sec.
Hence cost of boiling 4 cups of water
(b)
Given,
Initial temperature, θ1 = 5°C
Final temperature, θ2 = 100°C
Change in temperature, θ = θ2 − θ1 = 95°C
heat required for boiling water,
Where
m is the mass of the water
s is the specific heat of the water
θ is the change in temperature
Putting the value in the above formula, we get
= 0.8 × 4200 × 95
= 319200
Again converting into watt-second,
Cost of boiling 4 cups of water
=11000×3600×319200
= Rs 0.09