The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 `Omega` and at steam point is `5.39 Omega`. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 5.795 `Omega`. Calculate the temperature of the bath.

Explanation

Here, `T_(0) ` = ice point = `0^(@) C, R_(0) = 5 Omega`
`T_(1) = ` steam point = `100^(@)C, " " R_(1) = 5.23 Omega`
`T_(2) = ?, R_(2) = 5.795 Omega `
`R_(1) = R_(0) { 1 + alpha (T_(1) - T_(0))} `
`therefore 5.23 = 5 { 1 + alpha (100 - 0 )} `
`therefore 1.046 = 1 + alpha (100)`
`therefore 0.046 = alpha (100) " "` .... (1)
`R_(2) = R_(0) {1 + alpha (T_(2) - 0) }`
`5.795 = 5 { 1 + alpha (T_(2) - 0)} `
` therefore 1.159 = 1 + alpha (T_(2))`
` therefore 0.159 = alpha (T_(2)) " " ` ... (2)
Taking ratio of equations (1) and (2),
0.2893 = `(100)/(T_(2))`
`therefore T_(2) = (100)/(0.2893) = 345.7^(@) C `