The electrical resistance of pure platinum increases linearly with increasing temperature over a small range of temperature . This property is used in a Platinum resistance thermometer. The relation between `R_(theta)` (Resistance at `theta` K) and `R_(0)` (Resistance at `theta_(0)K`) is given by `R_(theta)=R_(0)[1+a(theta-theta_(0))]`, where `alpha=` temperature coefficient of resistance. Now, if a Platinum resistance thermometer reads `0^(@)C` when its resistance is `80Omega` and `100^(@)C` when its resistance is `90 Omega` find the temperature at which its resistance is `86Omega`.

Explanation

Using the given relationship
we have `(90-80)Omega=alpha(80 Omega)(100)`………..(i)
`(86-80)Omega=alpha(80 Omega)(theta)`………..(ii)
where `theta` is the desired temperature.
Taking the ratio of (i) and (ii)
`10/6=100/(theta)impliestheta=60K`