What is the change in area (in cm^2 ) of a 60.0 \ cm by 150 \ cm automobile windshield when the...

Question:

What is the change in area (in {eq}cm^2 {/eq}) of a {eq}60.0 \ cm {/eq} by {eq}150 \ cm {/eq} automobile windshield when the temperature changes from {eq}0 {/eq} to {eq}36.0^o C {/eq}? The coefficient of linear expansion of this glass is {eq}9.0 \times 10^{-6}/ ^oC {/eq}.

Linear Expansion:

It can be defined as the variation in the length of any object due to the variation in the temperature. It generally depends on the original length of the object, the difference in the temperature, and the coefficient of thermal expansion.

Given data:

• Initial temperature, {eq}{T_1} = 0{\rm{^\circ C}} {/eq}
• Final temperature, {eq}{T_2} = 36.0{\rm{^\circ C}} {/eq}
• Initial Area, {eq}{A_o} = 60.0 \times 150\;{\rm{c}}{{\rm{m}}^{\rm{2}}} {/eq}
• Coefficient of linear expansion, {eq}\alpha = 9.0 \times {10^{ - 6}}\;{\rm{^\circ }}{{\rm{C}}^{{\rm{ - 1}}}} {/eq}

The change in area can be calculated as,

{eq}\Delta A = {A_o}\alpha \left( {{T_2} - {T_1}} \right) {/eq}

Substitute the values,

{eq}\begin{align*} \Delta A &= 60 \times 150 \times 9 \times {10^{ - 6}} \times \left( {36 - 0} \right)\\ \Delta A &= 2.92\;{\rm{c}}{{\rm{m}}^{\rm{2}}} \end{align*} {/eq}

Therefore, the change in area is {eq}2.92\;{\rm{c}}{{\rm{m}}^{\rm{2}}} {/eq} .