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 and 24 ×100–6°C–1 , respectively.
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The size of the aluminium frame should be 20,012 cm by 30,018 cm so that there is no stress on the glass in winter even if the temperature drops to 0°C
Explanation:
Given:
At 40°C the glass window is 20 cm long and 30 cm wide, respectively.
Linear expansion coefficient for glass,
Linear expansion ratio for aluminium,
The final aluminium length should be equal to the final glass length so there is no tension on the glass in winter, Even if temperatures go down to 0 ° C.
Change in temperature,
Δθ = 40 °C
Let the initial aluminium length be
Let aluminium initial breadth be b.
The aluminium frame size should therefore be 20,012 cm by 30,018 cm.
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