Question

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

• A. 21.2 cc
• B. 15.2 cc
• C. 1.52 cc
• D. 2.12 cc

Answer 1

The correct option is B

15.2 cc

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

$△V=V_0[{\gamma }_t-{\gamma }_g]△\theta$

Given $V_0=1000cc,{\alpha }_0=0.1\times {10}^{-4\circ }C$

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

$\therefore △V=1000[1.82\times {10}^{-4}$
$-0.3\times {10}^{-4}]\times 100=15.2cc$