The resistance of platinum wire at $0 °\mathrm{C}$ is $2 \mathrm{\Omega }$ and $6.8 \mathrm{\Omega }$ at $80 °\mathrm{C}$. The temperature coefficient of resistance of the wire is:

The variation of resistance of a conducting metal with temperature is given by

$R_T=R_0\left(1+\alpha \left(T_2-T_1\right)\right) ...\left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to calculate the required temperature coefficient.

$\begin{array}{rcl}6.8 \mathrm{\Omega }& =& 2 \mathrm{\Omega }\times \left(1+\alpha \left(80-0\right)° \mathrm{C}\right)\\ & \Rightarrow & 1+80\alpha =3.4\\ & \Rightarrow & 80\alpha =2.4\\ & \Rightarrow & \alpha =3\times {10}^{-2} {\mathrm{C}}^{-1}\end{array}$