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 $m_0$m0​ and an initial temperature of $T_0$T0​. It is assumed that the water reaches a temperature of $T_1$T1​ in 8 minutes and 30 seconds, at which point heating is stopped.

Assume that $\eta_0$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, $c_w$cw​, is constant regardless of temperature.

Constraints

• $\eta_0 = 0.42$η0​=0.42 ($42\%$42%)
• $m_0 = 5950\ \mathrm{g}$m0​=5950 g
• $T_0 = 285\ \mathrm{K}$T0​=285 K
• $T_1 = 330\ \mathrm{K}$T1​=330 K
• $c_w = 4.184\ \mathrm{J}/(\mathrm{g}\cdot\mathrm{K})$cw​=4.184 J/(g⋅K)

Input Format

Let the calculated average power consumption be $A_1\ \mathrm{W}$A1​ W. Find the integer that is 10 times the value of $A_1$A1​, and enter that natural number.