Answer
The initial temperature of the water was $73.5^{\circ}C$
Work Step by Step
We can find the mass of the water as:
$m_w = \rho~V$
$m_w = (1000~kg/m^3)(200~mL)(\frac{1~m^3}{10^6~mL})$
$m_w = 0.200~kg$
The heat energy lost by the water will be equal to the heat energy gained by the glass thermometer. We can find the initial temperature of the water:
$m_w~c_w~\Delta T_w = m_g~c_g~\Delta T_g$
$m_w~c_w~(T - 71.2^{\circ}C) = m_g~c_g~\Delta T_g$
$m_w~c_w~T = m_g~c_g~\Delta T_g+m_w~c_w~(71.2^{\circ}C)$
$T = \frac{m_g~c_g~\Delta T_g+m_w~c_w~(71.2^{\circ}C)}{m_w~c_w}$
$T = \frac{(0.0500~kg)(750~J/kg~C^{\circ})(71.2^{\circ}C-20.0^{\circ}C)+(0.200~kg)(4186~J/kg~C^{\circ})(71.2^{\circ}C)}{(0.200~kg)(4186~J/kg~C^{\circ})}$
$T = 73.5~^{\circ}C$
The initial temperature of the water was $73.5^{\circ}C$.
