A piston-cylinder assembly containing a gas undergoes a process in which the temperature of the system rises from \(100^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\). The heat transmission per degree rise in temperature is governed by the equation

\[ \frac{d Q}{d T}=1.25 \frac{\mathrm{kJ}}{\mathrm{K}} \]

The work done on the system per degree rise in temperature is given by

\[ \frac{d W}{d T}=(5-0.25 T) \frac{\mathrm{kJ}}{\mathrm{K}} \]

Calculate the change in internal energy of the system during the process.