A thermocouple is connected across a battery, and a current flows through it. The cold junction is connected to a reservoir at \(0{ }^{\circ} \mathrm{C}\). When its hot junction is connected to a reservoir at \(100^{\circ} \mathrm{C}\) the heat flux due to the Peltier effect is \(2.68 \mathrm{~mW} / \mathrm{A}\), and when the hot junction is at \(200{ }^{\circ} \mathrm{C}\) the effect is \(4.11 \mathrm{~mW} / \mathrm{A}\). If the emf of the thermocouple due to the Seebeck effect is given by \(\varepsilon=a t+b t^{2}\), calculate the values of the constants \(a\) and \(b\). If the thermocouple is used to measure the temperature effect based on the Seebeck effect, i.e. there is no current flow, calculate the voltages at \(100{ }^{\circ} \mathrm{C}\) and \(200{ }^{\circ} \mathrm{C}\).

\(\left[5.679 \times 10^{-3} \mathrm{mV} / \mathrm{K} ; 7.526 \times 10^{-3} \mathrm{mV} /(\mathrm{K})^{2} ; 0.6432 \mathrm{mV} ; 1.437 \mathrm{mV}\right.\) ]