A cylinder closed by a free piston holds $4.0\ \text{g}$ of helium and $14.0\ \text{g}$ of nitrogen (rigid diatomic molecules), with molar masses $4\ \text{g/mol}$ and $28\ \text{g/mol}$. The mixture is heated slowly at constant pressure until its temperature has risen by $40\ \text{K}$. Take $R = 8.3\ \text{J/(mol K)}$. How much heat does the mixture take in? Give the answer in $\text{J}$.