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 . $ .



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