Q 11-10-022NEETJEE MainEAMCET 2013 (Engineering)Easy
A glass flask of volume one litre is filled completely with mercury at $0°$C. The flask is now heated to $100°$C. The coefficient of volume expansion of mercury is $1.82 \times 10^{-4}\ °\text{C}^{-1}$ and the coefficient of linear expansion of glass is $0.1 \times 10^{-4}\ °\text{C}^{-1}$. The amount of mercury which overflows is
Answer: (B) $15.2$ cc
Concept. Overflow $=$ real expansion of the mercury $-$ expansion of the flask: $\Delta V = V(\gamma_{Hg} - 3\alpha_g)\Delta T$.
Step 1. Substitute. $V = 1000$ cc:
$$\Delta V = 1000 \times (1.82 - 0.3) \times 10^{-4} \times 100 = 15.2\ \text{cc}$$
Answer. $15.2$ cc (Option B).
Solution by Sreeraj P, M.Sc Physics