A glass flask has a capacity of 60 cm³ at 12 °C. Calculate the capacity of the flask at a temperature of 50 °C if the glass has a linear coefficient of expansion of 9 × 10°/°C.
First, we need to calculate the expansion of the glass flask from 12 °C to 50 °C.
The formula for linear expansion is:
Change in length = initial length x coefficient of linear expansion x change in temperature
Since the volume of the flask is given, we will use the formula for volume expansion which is:
Change in volume = initial volume x coefficient of linear expansion x change in temperature
Given:
Initial volume = 60 cm³
Coefficient of linear expansion = 9 x 10^-6 /°C
Change in temperature = 50 °C - 12 °C = 38 °C
Now, we can calculate the change in volume:
Change in volume = 60 cm³ x 9 x 10^-6 /°C x 38 °C
Change in volume = 0.02052 cm³
To find the final capacity of the flask at 50 °C, we need to add the change in volume to the initial volume:
Final volume = 60 cm³ + 0.02052 cm³
Final volume = 60.02052 cm³
Therefore, the capacity of the flask at a temperature of 50 °C is approximately 60.02 cm³.