The readings of a constant volume gas thermometer at `0^(@)C and 100^(@)C` are 40 cm of mercury and 60 cm of mercury. If its reading at an unknown temperature is 100 cm of mercury column, then the temperature is :

Options

A. `100^(@)C`
B. `50^(@)C`
C. `25^(@)C`
D. `300^(@)C`

Answer

D

Explanation

Pressure at `0^(@)C, P_(0)=40cm`
Pressure at `100^(@)C, P_(100)=60cm`
Pressure at unknown temperature t,
`P_(t)=1000cm` of mercury. Then
`" "t=100((P_(t)-P_(0))/(P_(100)-P_(0)))`
`" "=100((100-40)/(60-40))=300^(@)C`