Question

A glass flask of volume one litre at $0^o$C is filled level full of mercury at this temperature. The flask and mercury are now heated to ${100}^o$C. How much mercury will spill out, if coefficient of volume expansion of mercury is $1.2\times {10}^{-4}{/}^o$C and linear expansion of glass is $0.1\times {10}^{-4}{/}^o$C, respectively?

• A. $2.48\times {10}^{-2}$L
• B. $1.52\times {10}^{-2}$L
• C. $1.53\times {10}^4$L
• D. $1.52\times {10}^{-4}$L

Answer 1

Answer: (B)

$1.52\times {10}^{-2}$L

Expansion of mercury
$\Delta V_m=V_m{\gamma }_m\Delta \theta$
$=1\times 1.82\times {10}^{-4}({100}^o-0^o)$
$=1.82\times {10}^{-2}$L
Expansion of flask,
$\Delta V_o=V{\gamma }_o\Delta \theta =V\cdot 3{\alpha }_g\Delta \theta$
$=1\times 3\times 0.1\times {10}^{-4}({100}^o-0^o)$
$=0.3\times {10}^{-2}$L
Volume of mercury that over flows
$=\Delta V_m-\Delta V_g$
$=(182-0.3)\times {10}^{-2}$
$=1.52\times {10}^{-2}$L.