A glass flask of volume one litre at 0^oC is filled, level full o… - Vidyadip

MCQ

A glass flask of volume one litre at $0^oC$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100°C$ ........... $cc$ mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times {10^{ - 4}}°C^{-1}$ and linear expansion of glass is $0.1 \times {10^{ - 4}}°C^{-1}$ respectively

A
$21.2$
✓
$15.2$
C
$1.52$
D
$2.12$

✓

Answer

Correct option: B.

$15.2$

b
(b) Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by

$\Delta V = {V_0}[{\gamma _L} - {\gamma _g}]\Delta \theta $

Given $V_0 = 1000 \,cc, \alpha_g ={ 0.1×10^{-4}} °C^{-1}$

${\gamma _g} = 3{\alpha _g} = 3 \times 0.1 \times {10^{ - 4}}°C^{-1} = 0.3 \times {10^{ - 4}}°C^{-1}$

$\Delta V = 1000 [1.82 × 10^{-4} -0.3 × 10^{-4}] × 100 = 15.2\, cc$

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