Answer
(a) It takes 4.43 hours to reach the boiling point.
(b) It takes another 28.4 hours to change all the boiling water to steam, for a total time of 32.8 hours.
Work Step by Step
(a) The energy $Q$ required to raise the temperature of a substance is:
$Q = mc~\Delta T$
We can find the heat energy required to raise the temperature of the water and the iron boiler.
$Q = m_w~c_w~\Delta T + m_i~c_i~\Delta T$
$Q = (730~kg)(4186~J/kg~C^{\circ})(100~^{\circ}C-18~^{\circ}C) + (180~kg)(450~J/kg~C^{\circ})(100~^{\circ}C-18~^{\circ}C) $
$Q = 2.57\times 10^8~J$
We can find the time required to reach the boiling point.
$t = \frac{Q}{P}$
$t = \frac{2.57\times 10^8~J}{5.80\times 10^7~J/hr}$
$t =4.43~hr$
It takes 4.43 hours to reach the boiling point.
(b) The energy $Q$ required to change the state of a substance is:
$Q = m~L$
We can find the heat energy required to change the boiling water to steam.
$Q = m_w~L$
$Q = (730~kg)(2.26\times 10^6~J/kg)$
$Q = 1.65\times 10^9~J$
We can find the time required to change the boiling water to steam:
$t = \frac{Q}{P}$
$t = \frac{1.65\times 10^9~J}{5.80\times 10^7~J/hr}$
$t =28.4~hr$
It takes another 28.4 hours to change all the boiling water to steam, for a total time of 32.8 hours.