Question

An aluminum cup of 140 cm3 capacity is completely filled with glycerin at 20°C. How much glycerin will spill out of the cup if the temperature of both the cup and glycerin is increased to 31°C? (The linear expansion coefficient of aluminum is 23 × 10-6 1/C°. The coefficient of volume expansion of glycerin is 5.1 × 10-4 1/C°.)

Answer 1

Explanation:

The given data is as follows.

    coefficient of volume expansion of glycerin ($\beta$) = $5.1 \times 10^{-4} 1/^{o}C$

     linear expansion coefficient of aluminum, $(\alpha_{A})$ = $23 \times 10^{-6} 1/^{o}C$  

              Volume = 100 $cm^{3}$

The increase in volume of the cup will be calculated as follows.

                    $\Delta V_{c} = V \times 3 \times \alpha \times \Delta T$

                                 = $100 cm^{3} \times 3 \times 23 \times 10^{-6} \times (31 - 20)^{o}C$

                                 = $75900 \times 10^{-6} cm^{3}$

                                 = 0.0759 $cm^{3}$

Formula for increase in volume  of glycerine is as follows.

               $\Delta V_{g} = V \times \beta_{g} \times \Delta T$

                              = $100 cm^{3} \times 5.1 \times 10^{-4} 1/^{o}C \times (31 - 20)^{o}C$

                              = 0.5610 $cm^{3}$

Therefore, volume of glycerin spilled is calculated as follows.

                        $\Delta V = \Delta V_{g} - \Delta V_{c}$

                                     = (0.5610 - 0.0759) $cm^{3}$

                                     = 0.4851 $cm^{3}$

Thus, we can conclude that 0.4851 $cm^{3}$ glycerin will spill out of the cup.