A resistance thermometer measures temperature with the increase in resistance of a wire of high temperature. If the wire is platinum and has resistance of `10Omega` at `20^@C` and a resistance of `35Omega` in a hot furnace, what is the temperature of the hot furnace? `(alpha_("platinum") = 0.0036^@C^(-1))`

Explanation

To solve the problem of finding the temperature of the hot furnace using the resistance of a platinum wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Initial resistance at \(20^\circ C\) (R_initial): \(10 \, \Omega\)
- Final resistance in the hot furnace (R_final): \(35 \, \Omega\)
- Temperature coefficient of resistance for platinum (\(\alpha\)): \(0.0036 \, ^\circ C^{-1}\)
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