Properties Of Solids And Liquids Question 406
Question: Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from $ 0{}^\circ C $ to $ 100{}^\circ C $ . A flask made of the same glass as that of rod measures a volume of 1000 cc at $ 0{}^\circ C $ . The volume it measures at $ 100{}^\circ C $ in cc is
Options:
A) 1002.4
B) 1004.2
C) 1006.4
D) 1008.2
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ T _{1}= 0{}^\circ C, T _{2}= 100{}^\circ C $
$ \gamma =\frac{V _{2}-V _{1}}{100V _{1}};\alpha =\frac{{\ell _{2}}-{\ell _{1}}}{100{\ell _{1}}} $
$ {\ell _{1}}=10cm;{\ell _{2}}-{\ell _{1}}=0.08mm=0.008cm $
$ \alpha =\frac{0.008}{10\times 100}=8\times {{10}^{-6}}{{/}^{o}}C $
$ \gamma =3\alpha =24\times {{10}^{-6}}{{/}^{o}}C $
$ \therefore 24\times {{10}^{-6}}=\frac{V _{2}-1000}{1000\times 100} $
$ V _{2}-1000\times 24\times {{10}^{-6}}\times 10^{5}=2.4 $
$ \therefore V _{2}=1002.4cc $
