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An electric kettle takes 4 A current at 220 V. How much time will it take to boil 1 kg of water from temperature $20^\circ C$ ? The temperature of boiling water is $100^\circ C$.
A
12.6 min
B
4.2 min
C
6.3 min
D
8.4 min
Detailed Solution
Heat required to boil the water: $Q = mc\,\Delta T$
$Q = 1 \times 1 \times (100 - 20) = 80$ kcal
In joules, taking $c = 4200$ J kg$^{-1}$ K$^{-1}$: $Q = 1 \times 4200 \times 80 = 336000$ J
Heat given by the supply in time $t$: $H = V\,i\,t = 220 \times 4 \times t = 880\,t$ J
Setting $H = Q$:
$880\,t = 336000$
$t = \dfrac{336000}{880} = 381.8$ s
$t = \dfrac{381.8}{60} \approx 6.3$ min
So the kettle takes about 6.3 min to boil the water.
$Q = 1 \times 1 \times (100 - 20) = 80$ kcal
In joules, taking $c = 4200$ J kg$^{-1}$ K$^{-1}$: $Q = 1 \times 4200 \times 80 = 336000$ J
Heat given by the supply in time $t$: $H = V\,i\,t = 220 \times 4 \times t = 880\,t$ J
Setting $H = Q$:
$880\,t = 336000$
$t = \dfrac{336000}{880} = 381.8$ s
$t = \dfrac{381.8}{60} \approx 6.3$ min
So the kettle takes about 6.3 min to boil the water.