Main Answer
The coefficient of volume expansion (α) is defined as the change in volume per unit volume per degree Celsius.The negative sign indicates that the coefficient of volume expansion is negative, meaning that the liquid contracts as it cools down, which is typical for many liquids at low temperatures. The value of the coefficient is approximately -0.0026 K^-1, which is relatively small but significant for liquids at low temperatures where the effect of volume expansion can be noticeable.
Step-by-step explanation
The coefficient of volume expansion is a measure of how much a liquid expands or contracts when its temperature changes. It is expressed as a fraction or percentage change in volume per unit change in temperature.
In this case, we have two known values: the initial volume and temperature, and the final volume and temperature. By calculating the change in volume and temperature, we can find the coefficient of volume expansion using the following formula:β = (ΔV / V0) / ΔT
where ΔV is the change in volume, V0 is the initial volume, and ΔT is the change in temperature. Let's apply this formula to our given scenario:
ΔV = Vfinal - Vinitial = 1.34 L - 1.54 L = -0.20 L
ΔT = Tfinal - Tinitial = 14.1 °C - 93.9 °C = -79.8 °C
β = (-0.20 L) / (-79.8 °C) = 0.0025 L / °C
So, our calculated coefficient of volume expansion is approximately 0.0025 L / °C, which is a very small value indicating that this liquid has a relatively low coefficient of volume expansion at these temperatures.
This means that this liquid does not expand or contract significantly when its temperature changes, which could be useful in certain applications where precise volumes are required over a wide range of temperatures.