The resistance of a thermometer is `100 Omega` at the triple point of water (`273 K) `and is `300 Omega` at the melting point of gold `(~873K).` The temperature at which the resistance of the thermometer is `200Omega` is

Options

A. 273 K
B. 373 K
C. 473 K
D. 573 K

Answer

D

Explanation

At `273 K or 0^(@)C,` resistance, `R_(0) =100 Omega`
At `873 K or 600^(@)C,` resistance `R_(600) = 300 Omega`
Now, let `theta` temperature resistance is given `R_(theta) = 200 Omega`
`thea =?`
By the formula, `theta = (R_(theta)-R_(0))/(R _(600) -R_(0))xx 600`
`theta = (200 -100)/( 300 -100) xx 600`
` theta = 300^(@)C`
`theta = 300+ 273 = 573 K`