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 Re 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?

#### Solution

Time taken to boil 4 cups of water, t = 2 minutes

Volume of water boiled = 4 × 200 cc = 800 cc

Initial temperature, θ_{1} = 25°C

Final temperature, θ_{2} = 100°C

Change in temperature, θ = θ_{2} − θ_{1} = 75°C

Mass of water to be boiled, m = 800 × 1 = 800 gm = 0.8 Kg

Heat required for boiling water,

Q = msθ = 0.8 × 4200 × 75 = 252000 J

We know:-

1000 watt - hour = 1000 × 3600 watt sec.

∴ Cost of boiling 4 cups of water

\[= \frac{1}{1000 \times 3600} \times 252000\]

= Rs. 0.7

(b) Initial temperature, θ_{1} = 5°C

Final temperature, θ_{2} = 100°C

Change in temperature, θ = θ_{2} − θ_{1} = 95°C

Q = msθ = 0.8 × 4200 × 95 = 319200

∴ Cost of boiling 4 cups of water

\[= \frac{1}{1000 \times 3600} \times 319200\]

= Rs. 0.09