Question

A glass bulb of volume 250cc is filled with mercury at 20${}^0$C and the temperature is raised to ${100}^{0}C$. If the coefficient of linear expansion of glass is $9\times {10}^{-6/0}C$ Coefficient of absolute expansion of mercury is $18\times {10}^{-4/0}C$. The volume of mercury that overflows is

• A. 35.46cc
• B. 29.4cc
• C. 36.12cc
• D. 27.73cc

Answer 1

Answer: (A)

35.46cc

${\gamma }_{glass}=3{\alpha }_{glass}=3\times 9\times {10}^{-6}=27\times {10}^{-6}$
${\gamma }_{mercury}=18\times {10}^{-4}$
Amount of mercury to overflow from the glass $V_{overflow}=V_0\times ({\gamma }_{mercury}-{\gamma }_{glass})\times \Delta T=250\times (18\times {10}^{-4}-27\times {10}^{-6})\times (100-20)=250\times 1773\times {10}^{-6}\times 80$

$⟹V_{overflow}=35.46cc$