Question

A glass bottle of volume $5\text{litres}$ is filled with gasoline at room temperature. Accidently, the bottle was left close to an engine exhaust and the temperature rises by ${40}^{\circ }\text{C}$. Calculate the volume of gasoline that spills out of the glass bottle as a result of this temperature rise.
[Take room temperature to be ${25}^{\circ }\text{C}$, coefficient of linear expansion of glass as $8.5\times {10}^{-6}{/}^{\circ }\text{C}$, volumetric coefficient of gasoline at ${25}^{\circ }\text{C}$ as $950\times {10}^{-6}{/}^{\circ }\text{C}$].

• A. $184.9\text{cc}$
• B. $184.9\text{liters}$
• C. $190\text{cc}$
• D. $5.1\text{cc}$

Answer 1

The correct option is A $184.9\text{cc}$

${\gamma }_{glass}=3{\alpha }_{glass}=3\times 8.5\times {10}^{-6}=25.5\times {10}^{-6}{/}^{\circ }\text{C}$
${\gamma }_{gasoline}=950\times {10}^{-6}{/}^{\circ }\text{C}$
Amount of gasoline that spills out from glass bottle
= volumetric expansion of gasoline - volumetric expansion of glass bottle
$=V\times {\gamma }_{\text{gasoline}}\times \Delta T-V\times {\gamma }_{\text{glass}}\times \Delta T$
$=V\left({\gamma }_{\text{gasoline}-{\gamma }_{\text{glass}}}\right)\Delta T$
$=5\times (950\times {10}^{-6}-25.5\times {10}^{-6})\times 40$
$=0.1849\text{liters}$
$=184.9\text{cc}$