A glass window is to be fit in an aluminium frame. The temperature on the working day is 40°C and the glass window measures exactly 20 cm × 30 cm. What should be the size of the aluminium frame so that there is no stress on the glass in winter even if the temperature drops to 0°C? Coefficients of linear expansion for glass and aluminium are 9.0 × 10–6 °C–1 & 24×10–6°C–1respectively.
Given:
Change in Temperature : ΔT= 40 ° C…( From- winter temperature is 0°C to working day temperature is 40°C)
Length of the Glass window : lGl= 20 cm
Breadth of the Glass Window: bGl = 30 cm.
Coefficient of linear expansion for glass :αgl = 9.0 × 10–6 °C-1
Coefficient of linear expansion for Aluminum: αAl=24×10–6°C-1.
Due to a drop in temperature, thermal contraction will take place(opposite of thermal expansion) and thus the dimensions of both aluminium frame and glass window will undergo contraction. In order to avoid crack in the glass window, the contracted size of both the frame and the window should be same.
Formula used:
We will see this numerically:
Formula for thermal contraction is:
Here, l’ is the changed length and the value of α is negative ( since its contraction).
Now,
Let the changed length of aluminium frame = Changed length of glass window.
Now,
Let the changed breadth of aluminium frame = Changed breadth of Glass window
Hence, the dimensions of the aluminium frame so that there is no stress on the glass in winter are 20.01 cm × 30.018 cm