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Answer to Question #117945 in Other Physics for Arogundade Moses Temitope

Question #117945
An electric kettle has a 750W-240V heater and is used on a 200V mains. if the heat capacity of the kettle is 400J/K and the initial water temperature is 20°C, how long will it take to boil 500g of water, assuming the resistance of the heater is Unaltered on changing to the new mains.
1
2020-05-25T11:16:49-0400

First, obtain the power of the kettle that is used at 200V-circuit:

@$R=\frac{V_1^2}{P_1}=\frac{V^2_2}{P_2},\\ \space\\ P_2=P_1\bigg(\frac{V_2^2}{V_1^2}\bigg)^2.@$

The amount of heat, on the one hand, is

@$Q=P_2t,@$

and, on the other hand, it is the heat required to heat the water and kettle up:

@$Q=\Delta \tau(cm+C).\\ \space\\ t=\frac{V_1^2\Delta \tau(cm+C)}{V_2^2P_1}=384\text{ s}.\\ @$

It is equivalent to 6 minutes and 24 seconds.

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