To determine how much glycerine will spill out of the aluminium cup when the temperature is raised from 22ºC to 28ºC, we need to consider the concept of thermal expansion. Both the glycerine and the cup will expand when heated, but they will do so at different rates due to their distinct coefficients of volume expansion. Let's break this down step by step.
Understanding Volume Expansion
When a substance is heated, its volume typically increases. This phenomenon is quantified by the coefficient of volume expansion, which tells us how much the volume of a substance will change per degree change in temperature. For glycerine, the coefficient of volume expansion is given as 5.1 × 10-4 /ºC.
Calculating the Volume Change of Glycerine
First, we need to calculate how much the volume of glycerine will expand when the temperature increases from 22ºC to 28ºC. The change in temperature (ΔT) is:
Next, we can use the formula for volume expansion:
ΔV = V₀ × β × ΔT
Where:
- ΔV = change in volume
- V₀ = initial volume of glycerine (110 cm3)
- β = coefficient of volume expansion (5.1 × 10-4 /ºC)
- ΔT = change in temperature (6ºC)
Plugging in the values:
ΔV = 110 cm3 × (5.1 × 10-4 /ºC) × 6ºC
ΔV = 110 cm3 × 0.00051 × 6
ΔV = 110 cm3 × 0.00306
ΔV ≈ 0.3366 cm3
Determining the New Volume of Glycerine
Now, we can find the new volume of glycerine after the temperature increase:
V_new = V₀ + ΔV
V_new = 110 cm3 + 0.3366 cm3 ≈ 110.3366 cm3
Considering the Capacity of the Cup
The aluminium cup has a capacity of 110 cm3. Since the new volume of glycerine (approximately 110.34 cm3) exceeds the cup's capacity, we need to calculate how much will spill out:
Spilled volume = V_new - Cup capacity
Spilled volume = 110.3366 cm3 - 110 cm3 ≈ 0.3366 cm3
Final Result
Therefore, when the temperature of the glycerine is raised from 22ºC to 28ºC, approximately 0.34 cm3 of glycerine will spill out of the aluminium cup. This example illustrates how thermal expansion can affect liquids in confined spaces, leading to potential overflow when temperatures rise.
