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Resistance thermometer . The variation i...

Resistance thermometer . The variation in electrical resistance with temperature can be used to make precise temperature measurements. Platinum is commonly used since it is relatively free from corrosive effects and has a high melting point. Suppose at `20.0 ^(@)C` the resistance of a platnum resistance thermometer is `164.2 Omega ` When praised in a particular solution, the resistance is`187.4 Omega ` . What is the temperature of this solution ?

Text Solution

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As `R = ( rho l)/(A) ` and `R_(0) = ( rho _(0)l)/(A), R = R_(0) [1+alpha(T-T_(0))]`
Here `R_(0) = rho _(0)L//A` is the resistance of the wire as `T_(0)= 20.0 ^(@)C ` . We solve this equation for T and find
`T= T_(0)+ (R-R_(0))/(alphR_(0))= 20.0^(@)C + ( 187.4 Omega - 164.2 Omega )/((3.927 xx 10^(-3)(C^(@))^(-1))(164.2 Omega))= 56.0 ^(@)C`
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