Answer
A minimum of $3000~J$ of heat energy must be removed to liquify the nitrogen.
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 that must be removed to lower the temperature of the nitrogen and change it into a liquid.
$Q = m~c~\Delta T-m~L$
$Q = (0.0070~kg)(1040~J/kg~C^{\circ})(-196~^{\circ}C-20^{\circ}C)-(0.0070~kg)(2.0\times 10^5~J/kg)$
$Q = -3000~J$
A minimum of $3000~J$ of heat energy must be removed to liquify the nitrogen.