This is related to the formula of change in the length on temperature change ΔL = L × α × ΔT Lets say we have a scale of 100 cm and lets say α is 10 -2 We increase the temperature from 20 to 30 degrees then ΔL = 100 × 10 -2 × (30 – 20) = 10 cm so the new length is L + ΔL = 100 + 10 = 110cm Now the scale is at a temperature of 30 degrees and now we decrease the temperature back to 20 degrees then ΔL = 110 × 10 -2 × (20 – 30) = 11 cm so the final length is L – ΔL = 110 – 11 = 99 cm So we can see that after increasing the temperature and then decreasing it back to its original temperature, the length of the scale has decreased from 100 to 99 cm. My question is how can length of the scale reduce Initially scale temp was 20 degrees, its length was 100 cm and finally also scale temp is 20 degrees but the length now is 99 cm.

This is related to the formula of change in the length on temperature change  ΔL = L × α × ΔT  

 

Lets say we have a scale of 100 cm and lets say α is 10^-2

We increase the temperature from 20 to 30 degrees

then ΔL = 100 × 10^-2 × (30 – 20) = 10 cm

so the new length is L + ΔL = 100 + 10 = 110cm

 

Now the scale is at a temperature of 30 degrees and now we decrease the temperature back to 20 degrees

then ΔL = 110 × 10^-2 × (20 – 30) = 11 cm

so the final length is L – ΔL = 110 – 11 = 99 cm

 

So we can see that after increasing the temperature and then decreasing it back to its original temperature, the length of the scale has decreased from 100 to 99 cm.

 

My question is how can length of the scale reduce 

Initially scale temp was 20 degrees, its length was 100 cm

and finally also scale temp is 20 degrees but the length now is 99 cm.