Properties Of Solids And Liquids Question 397
Question: If $ \alpha ,\beta $ and $ \gamma $ are coefficient of linear, area and volume expansion respectively, then
Options:
A) $ \gamma = 3\alpha $
B) $ \alpha = 3\gamma $
C) $ \beta = 3\alpha $
D) $ \gamma = 3\beta $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ V+\Delta V={{(L+\Delta L)}^{3}}={{(L+\alpha L\Delta T)}^{3}} $
$ =L^{3}+(1+3\alpha \Delta T+3{{\alpha }^{2}}\Delta T^{2}+{{\alpha }^{3}}\Delta T^{3}) $
$ \Rightarrow {{\alpha }^{2}} $ and $ {{\alpha }^{3}} $ terms are neglected. $ \therefore V(l+\gamma \Delta T)= V(1+3\alpha \Delta T) $
$ l+\gamma \Delta T=l+3\alpha \Delta T\therefore \gamma =3\alpha . $ .
