Answer
$6900~J$ of heat energy must be added to the mercury.
Work Step by Step
The heat energy $Q$ required to change the temperature of a substance is:
$Q = m~c~\Delta T$
The heat energy $Q$ required to change the state of a substance is:
$Q = m~L$
We can find the heat energy required to change the mercury into mercury vapor.
$Q = m~c~\Delta T + m~L$
$Q = (0.020~kg)(140~J/kg~C^{\circ})(357~^{\circ}C-20~^{\circ}C) + (0.020~kg)(2.96\times 10^5~J/kg)$
$Q = 6900~J$
$6900~J$ of heat energy must be added to the mercury.
