A glass window is to be fit in an aluminium farme. The temperature on the working day is `40^C` and the glass window measuers exactlt 20 cm xx 30 cm. What should be the size of the aluminium frame so that there is no stresson the glass in winter even if the pemperature drops to `0^C`? Coefficients of linear expansion for glass and aluminium are `9.0 xx 10^(-6) o^C(-1) respectively.

Explanation

The final length of Aluminium should be
equal to the final length of Glass
Let the initial length of Aluminium `= l`
`l(1-alpha_Al Delta theta)= 20(1-alpha_g Delta theta)`
`rArr (l(1-24 xx 10^-6 xx 40))`
`=20(1-9xx10^-6 xx 40)`
`rArr (1-0.00096)=20(1-0.0036)`
`rArr l=(20 xx 0.99964)/(1-0.00096)`
`=20 xx 0.99964/0.99904 =20.012 cm`
Let initial breadth of Aluminium `= b
`b(1-alpha_Al Delta theta) = 30(1-alpha_g Delta theta)`
`rArr b = 30 xx (1-9 xx 10^-6 xx 40)/(1-24 xx 10^6 xx 40) `
`=30 xx 0.99964/0.99904`
`=30.018 cm`