Chapter 13, Problem 83A

To determine

Change in volume of a $\text{1}\text{.0}{\text{m}}^3$ concrete block if its temperature is raised $45°\text{C}$ .

Answer to Problem 83A

Change in volume will be $1.6\times {10}^{-3}{\text{m}}^3$ .

Explanation of Solution

Given:

Volume of concrete block, $V\text{ = 1}{\text{.0 m}}^{\text{3}}$

Change in temperature, $\Delta T\text{= 45}°\text{C}$

Volume coefficient of expansion, $\beta {\text{ = 36×10}}^{\text{-6}}\text{per}°\text{C}$

Formula used:

Change in volume,

  $\text{Δ}V=\beta V\text{Δ}T$

Where, $\text{Δ}V$ is change in volume, $\beta$ is coefficient of volume expansion, $V$ is the volume, $\Delta T$ is the change in temperature.

Calculation:

  $\text{Δ}V=\beta V\text{Δ}T$

  $\text{Δ}V=36\times {10}^{-6}\text{per}°\text{C}\times 1{\text{m}}^3\times 45°\text{C}$

  $\Delta V=\text{1620}\times {\text{10}}^{-6}{\text{m}}^3$

  $\text{Δ}V=1.6\times {10}^{-3}{\text{m}}^3$

Conclusion:

Change in volume of a concrete block will be $1.6\times {10}^{-3}{\text{m}}^3$ .