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

Step-by-step explanation:

The given data is as follows.

coefficient of volume expansion of glycerin (
`\beta`) =
`5.1 * 10^(-4) 1/^(o)C`

linear expansion coefficient of aluminum,
`(\alpha_(A))` =
`23 * 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 * 3 * \alpha * \Delta T`

=
`100 cm^(3) * 3 * 23 * 10^(-6) * (31 - 20)^(o)C`

=
`75900 * 10^(-6) cm^(3)`

= 0.0759
`cm^(3)`

Formula for increase in volume of glycerine is as follows.

`\Delta V_(g) = V * \beta_(g) * \Delta T`

=
`100 cm^(3) * 5.1 * 10^(-4) 1/^(o)C * (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.