The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at steam point, it is 5.23 Ω. When the thermometer is inserted in a hot bath, the resistance of the platinum wire becomes 5.795 Ω. Find the temperature of the bath.

345.65°C

$ R = R_0 (1 + \alpha \Delta t)$

$ \alpha = \frac{R - R_0}{R_0\Delta t} = \frac{5.23 - 5}{500} = 4.6\times 10^{-4}$

$ R' = R_0 (1 + \alpha \Delta t) $

$ \Delta t = \frac{R-R_0}{R_0 \alpha} = \frac{0.795}{5\times 4.6\times 10^{-4}} = 345.65^oC$