91影视

1. Initial temperature before expansion,${\mathrm{T}}_1=20掳\text{C}$
2. Final temperature after expansion,${\mathrm{T}}_2=270掳\text{C}$
3. The linear coefficient of expansion,$\mathrm{伪}=11脳{10}^{鈭�6}/掳\text{鈥塁}$
4. Initial length before the expansion,${\mathrm{L}}_1=20.05\text{鈥塩尘}$
5. Final length after the expansion,${\mathrm{L}}_2=20.11\text{鈥塩尘}$

When an object's temperature changes, it expands and grows larger, a process known as thermal expansion. If the temperature of a metal rod of length L is raised by an amount$\mathbf{螖}\mathbf{\text{T}}$, its length is found to be increased by the amount$\mathit{螖}\mathbf{\text{L}}\mathbf{=}\mathbf{\text{L}}\mathit{伪}\mathit{螖}\mathbf{\text{T}}$where,$\mathit{伪}$is the coefficient of linear expansion of the material.

Formula:

The linear expansion of a body, $\mathbf{螖尝}\mathbf{=}\mathbf{尝伪}\mathbf{}\mathbf{螖罢}\mathbf{}$ 鈥�(颈)

where, $\mathrm{伪}$is the coefficient of linear expansion of body.

The change in length for the section of the steel ruler between its$\text{20.05cm}$mark and$\text{20.11cm}$ mark is given using equation (i) as:

$\begin{array}{c}\mathrm{螖尝}=\left(20.11\text{鈥塩尘}\right)(11脳{10}^{鈭�6}\text{鈥�}/掳\text{鈥塁})(270掳\text{C}鈭�20掳\text{C})\\ =0.0551\text{鈥塩尘}\end{array}$

Thus, the actual change in length for the rod is given as:

$\begin{array}{c}\mathrm{螖}\text{L}=(20.11鈭�20.05)\text{cm}+0.055\text{鈥塩尘}\\ =0.115\text{鈥塩尘}\end{array}$

The coefficient of thermal expansion for the material of which the rod is made using equation (i) is given as:

$\begin{array}{c}\mathrm{伪}=\frac{\mathrm{螖尝}}{\mathrm{L}鈰�\mathrm{螖罢}}\\ =\frac{0.115\text{鈥塩尘}}{20.05\text{鈥塩尘}鈰�(270鈭�20)掳\text{鈥塁}}\\ =23脳{10}^{鈭�6}/掳\text{鈥塁}\end{array}$

Hence, the value of the coefficient of linear expansion is$23脳{10}^{鈭�6}/掳\text{鈥塁}$