A steel rular exactly `20 cm` long is graduated to give correct measurements at `20^@C`.
(a) Will it give readings that are too long or too short at lower temperatures?
(b) What will be that actual length of the rular when it is used in the desert at a temperature of `40^@ C` ? `alpha_(steel) = 1.2 xx 10^-5(.^@ C)^-1` .

Explanation

If the temperature decreases, the length of the ruler alos decreases through thermal contration. Below `20^(@)C,` each centimetre division is actuallty somewhat shorter then `1.0` cm, so the steel ruler gives readings that are to long.
Given, temperature `DeltaT=T_(2)-T_(1)=40-20=20^(@)C` length `l= 20` cm
At `40^(@)C,` the increase in length of the ruler is
`Deltal=lalphaDelta T=(20)(1.2xx10^(-5))20^(@)C`
`=0.48xx10^(-2)` cm
`therefore` The actual length of the ruler is ,
`l'=l+Deltal=20+0.48xx10^(-2)=20.0048` cm