A faulty thermometer has its upper and lower fixed points marked as `104^(@)C and -4^(@)C`, respectively. What is the correct temperature if the above thermometer reads `32^(@)C` ?

Explanation

Use the following relation `((S-LEP)/(UFP-LFP))_("Faulty scale")=((S-LFP)/(UFP-LFP))_("Correctscale")`
Substituting
`((S-LFP)/(UFP-LFP))_("Faulty scale")=[(32-(-4))/(104-(-4))]`
`=(36)/(108)=(1)/(3)" (1)"`
and
`((S-LFP)/(UFP-LFP))_("Correct scale")=(S-0)/(100-0)`
`(S)/(100)" (2)"`
Equating and solving (1) and (2), we get
`(S)/(100)=(1)/(3)`
`rArr" "S=(100)/(3)=33.33^(@)C` (approximately)