Question

Coefficient of linear expansion of a crystal in 3 mutually perpendicular directions are $8.5\times {10}^{-6}{/}^{o}C,10.5\times {10}^{-6}{/}^{o}C,11\times {10}^{-6}{/}^{o}C$. If mass of crystal is $25gm$, its volume at ${60}^{o}C$ is (given density at $0^{o}C$ is $5gm/cc$) :

• A. 5.009 cc
• B. 4.991 cc
• C. 5.9 cc
• D. 5.999 cc

Answer 1

The correct option is A 5.009 cc

In this case, value of $\gamma =(8.5+10.5+11){10}^{-6}=30\times {10}^{-6}$
Volume at $0^0$ $C=25/5=5cc$
Now, $V_{60}=V_0(1+\gamma dt)$ where dt = change in temperature $={60}^{0}C$
Putting all the values we get, $V_{60}=5.009$