The coefficient of cubical expansion of mercury is 0.00018
Question :- The coefficient of cubical expansion of mercury is 0.00018/ºC and that of brass 0.00006/ºC. If a barometer having a brass scale were to read 74.5 cm at 30 ºC, find the true barometric height at 0 ºC. The scale is supposed to be correct at 15 ºC.
(A) 74.122 cm
(B) 79.152 cm
(C) 42.161 cm
(D) 142.39 cm
Solution :
γbrass = 0.00006/ºC
⇒ αbrass = 0.00002/ºC
Using
![\displaystyle {{h}_{true}}={{h}_{observed}}\left[ 1+{{\alpha }_{scale}}\left( {{T}_{t}}-{{T}_{cal}} \right)-{{\gamma }_{Hg}}\left( {{T}_{t}}-{{T}_{0}} \right) \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%7B%7Bh%7D_%7Btrue%7D%7D%3D%7B%7Bh%7D_%7Bobserved%7D%7D%5Cleft%5B+1%2B%7B%7B%5Calpha+%7D_%7Bscale%7D%7D%5Cleft%28+%7B%7BT%7D_%7Bt%7D%7D-%7B%7BT%7D_%7Bcal%7D%7D+%5Cright%29-%7B%7B%5Cgamma+%7D_%7BHg%7D%7D%5Cleft%28+%7B%7BT%7D_%7Bt%7D%7D-%7B%7BT%7D_%7B0%7D%7D+%5Cright%29+%5Cright%5D&bg=ffffff&fg=000&s=0&c=20201002 "The coefficient of cubical expansion of mercury is 0.00018 1")
![\displaystyle \Rightarrow {{h}_{true}}=74.5\left[ 1+0.00002\times \left( 30-15 \right)-0.00018\times \left( 30-0 \right) \right]](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5CRightarrow+%7B%7Bh%7D_%7Btrue%7D%7D%3D74.5%5Cleft%5B+1%2B0.00002%5Ctimes+%5Cleft%28+30-15+%5Cright%29-0.00018%5Ctimes+%5Cleft%28+30-0+%5Cright%29+%5Cright%5D&bg=ffffff&fg=000&s=0&c=20201002 "The coefficient of cubical expansion of mercury is 0.00018 2")
So (A) is the correct option.
Read complete article – Error in Metal Scale Reading Due To Expansion and Contraction