What amount of heat must be supplied to \(2.0\times 10^{-2}~\text{kg}\) of nitrogen (at room temperature) to raise its temperature by \(45~^{\circ}\text{C}\) at constant pressure? (Molecular mass of \(N_2 =28,~R= 8.314~\text{J mol}^{-1}\text{K}^{-1}\)${\mathrm{}}^{}$).
1. \(935~\text{J}\)
2. \(934~\text{J}\)
3. \(936~\text{J}\)
4. \(930~\text{J}\)

A cylinder with a movable piston contains \(3\) moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?