A thermocouple using iron and copper produces an emf of $E_1$ when its junctions are kept at $0^\circ C$ and $100^\circ C$. If the cold junction is kept at $-20^\circ C$ and the emf is $E_2$, what is the temperature of the hot junction?

The resistance of the wire in the platinum resistance thermometer at ice point is 5$\Omega$ and at steam point is 5.25$\Omega$.When the thermometer is inserted in an unknown hot bath its resistance is found to be 5.5$\Omega$. The temperature of the hot bath is