GWCB002 Question 4
Problem Statement
Boiling Water with an IH Cooktop and a Kettle from Another Dimension
Problem Statement
While Person A was boiling water in an electric kettle as usual, the kettle suddenly exploded for some unknown reason (see the explanation for Question 3 for details), so Person A had no choice but to boil water using an IH cooktop and a kettle instead.
The volume of water boiled in the kettle has a mass of m0 and an initial temperature of T0. It is assumed that the water reaches a temperature of T1 in 8 minutes and 30 seconds, at which point heating is stopped.
Assume that η0 is the proportion (thermal efficiency) of the thermal energy generated by the induction cooktop that is used to heat the kettle and the water as a whole, rather than escaping to the outside. Note that the heat capacity of the kettle is negligible, and the specific heat capacity of water, cw, is constant regardless of temperature.
Constraints
- η0=0.42 (42%)
- m0=5950 g
- T0=285 K
- T1=330 K
- cw=4.184 J/(g⋅K)
Input Format
Let the calculated average power consumption be A1 W. Find the integer that is 10 times the value of A1, and enter that natural number.
Solution
Explanation
Calculation of Heat
The heat Q J absorbed by a mass of m g of water to raise its temperature by ΔT K is represented by the following relationship, where the specific heat is cw J/(g⋅K):
Q=mcwΔT
The temperature change ΔT in this problem is calculated as follows.
ΔT=T1−T0=330−285=45 K
Substituting the values from the constraint column, the actual heat energy absorbed by the water, Q, is as follows.
Q=5950×4.184×45=1120266 J
Calculation of the heating appliance's energy consumption and power consumption
Since the thermal efficiency is η0=0.42, the total energy output W J of the heating appliance (induction cooktop) is related to the heat absorbed by the water Q J by the relationship Q=η0W. Therefore, W can be calculated as follows.
W=η0Q=0.421120266=2667300 J
The heating time was “8 minutes 30 seconds.” We convert this to seconds.
t=8×60+30=510 s
The average power (rate of work) A1 W is obtained by dividing the total energy W by the time t.
A1=tW=5102667300=5230 W
Calculation of the Input Format
The required value is the integer obtained by multiplying the average power consumption A1 by 10.
A1×10=5230×10=52300
The final input integer is 52300.