Question

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.

Answer 1

Explanation:

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Answer 2

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,

$\alpha_g= 9.0 \times 10^{-6} ^{\circ}C^{-1}$

Linear expansion ratio for aluminium,

$\alpha{Al} = 24 \times 100^{-6}$   $^{\circ}C^{-1}$

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

$l\left(1-\alpha_{A l} \Delta \theta\right)=20\left(1-\alpha_{g} \Delta \theta\right)$

$l(1-24 \times 10-6 \times 40) &=20(1-9 \times 10-6 \times 40)$

$l(1-0.00096) &=20(1-0.00036)$

$l=20 \times & \frac{0.99964}{1-0.00096}$

$l =& 20 \times \frac{0.99964}{0.99904}$

$l &=20.012 \mathrm{cm}$

Let aluminium initial breadth be b.

$B\left(1-\alpha_{A 1} \Delta \theta\right)=30\left(1-\alpha_{g} \Delta \theta\right)$

$\left.b=\frac{30 \times(1-9 \times 10-6 \times 40}{(1-24 \times 10-6 \times 40)}$

$b=\frac{30(1-90-240)}{(1-240-240)}$

$=30 \times \frac{0.99964}{0.99904}$

$b=30.018 \mathrm{cm}$

The aluminium frame size should therefore be 20,012 cm by 30,018 cm.