A glass vessel is completely filled with 60 cm³ of mercury at 18 °C. The temperature of the (5) any glass vessel and its content increases to 60 °C. The linear coefficient of expansion of glass is 9 x 10-6/°C, and the volumetric expansion of mercury is 180 × 10-6/°C. Calculate: a) The volume of the glass vessel at 60 °C.
To calculate the volume of the glass vessel at 60 °C, we first need to find the volume of mercury at 60 °C and then subtract it from the total volume to find the volume of the glass vessel.
Given that the initial volume of mercury is 60 cm³, we can calculate the new volume of mercury at 60 °C using the formula for volumetric expansion:
Vf = Vi(1 + βΔT)
Where:
Vf = final volume
Vi = initial volume
β = volumetric expansion coefficient
ΔT = change in temperature
Plugging in the values, we get:
Vf = 60 cm³(1 + 180 × 10-6 × (60 - 18)) = 60(1 + 0.0108) = 60.648 cm³
Next, we can calculate the total volume at 60 °C by adding the volume of mercury to the volume of the glass vessel:
Vtotal = Vglass + Vf
We can calculate the volume of the glass vessel by using the linear expansion formula and then subtracting the volume of mercury:
ΔV = ViαΔT
ΔVglass = ViαΔTglass = 60 cm³ * 9 x 10-6 * (60-18) = 0.01908 cm³
Now, we can calculate the volume of the glass vessel at 60 °C:
Vglass60 = Vglass18 + ΔVglass = 60 cm³ + 0.01908 cm³ = 60.01908 cm³
Therefore, the volume of the glass vessel at 60 °C is 60.01908 cm³.