Question

A concrete slab has a length of 10 m on a winter night when the temperature is 0°C. Find the length of the slab on a summer day when the temperature is 35­°C. The coefficient of linear expansion of concrete is 1.0 × 10–5 °C–1.

Answer 1

So, the length of the slab at $35\°C$ is $\textrm{10.0035 m}$

Explanation:

$\textrm{The length of the lab, } L_i =\textrm{ 10 m}$ at $T_i = 0 \°C$

$\textrm{The length of the lab, } L_f =$ ? at $T_f = 35 \°C$

$\textrm{Change in temperature of slab,}[tex] [tex] \DeltaT = T_f - T_i = 35- 0 = 35 \°C$

$\textrm{Coefficient of linear expansion, }$$\alpha = 1.0\times10^{-5}\°C^{-1}$

The relation between the length of the road at any other temperature is given by  

$\alpha\Delta T = \textrm{thermal strain}$

$\alpha\Delta T = \frac{\textrm{Change in length}}{\textrm{Initial length}}$

$l_f = l_i(1 + \alpha \Delta T)$

$l_f = 10(1 + 1\times 10^{-5}\times35)$

$l_f = \textrm{10.0035 m}$

So, the length of the slab at $35\°C$is $\textrm{10.0035 m}$

Answer 2

Length of Slab is 10.0035 m

Explanation:

Given:

• Length of the slab when the temperature is 0°C,  $L_0$ = 10 m

• The temperature on the summer day, t = 35­ °C

Let be the length of the slab on a summer day when the temperature is 35°C.

• The coefficient of linear expansion of concrete, $a = 1 \times 10^-^5 C^-^1$

$L_1 = L_0 (1 + \alpha t)$

or $L_1 = 10(1 + 10^-^5 \times 35)$

or $L_1 = 10 + 35 \times 10^-^4$

So, $L_1 = 10.0035 m$

So, the length of the slab on summer day when the temperature is 35°C is 10.0035 m.