Answer to Question #117945 in 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
Expert's answer
2020-05-27T10:51:36-0400

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


R=V12P1=V22P2, P2=P1(V22V12)2.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=P2t,Q=P_2t,

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


cc is specific (per 1 kg of substance) heat capacity of water, 4200 J/(kg K).

mm is mass of the water, 0.5 kg.

CC is heat capacity of the kettle, 400 J/K.

Indeed, to boil the water, we must heat 0.5 kg of water from 20 to 100°C. The heat required for this is


Qw=cmΔτ.Q_w=cm\Delta \tau.

Also, heating the kettle from 20 to 100°C requires thermal energy


Qk=CΔτ,Q_k=C\Delta \tau,

therefore, the total energy required is


Q=Qw+Qk=Δτ(cm+C). t=V12Δτ(cm+C)V22P1=384 s.Q=Q_w+Q_k=\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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Comments

Arogundade Moses Temitope
26.05.20, 00:08

Ok following this illustration what is our "cm" and "C" denotes

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