Question

A glass block of 10 000cm3

volume is heated from 25oC to 40oC. The volume is found to

increase by 4cm3

Calculate the coefficient of cubical expansion of glass.

Answer 1

A temperature change $\Delta T$ causes a change in any linear dimension $L_0$ of a solid body. The change ΔL is approximately proportional to $L_0$ and ΔT. Similarly, a temperature change causes a change ΔV in the volume $V_0$ of any solid or liquid; ΔV is approximately proportional to $V_0$ and ΔT. The quantities $\alpha$ and $\beta$ are the coefficients of linear expansion and volume expansion, respectively. For solids, $\beta=3\alpha=\frac{\Delta V}{V_0\,\Delta T}$.

Using $V_0=10000\,{cm}^3=10^4\,{cm}^3$, $\Delta T = (40-25)°C=(313.15-298.15)K=15\,K$ and $\Delta V=4\,{cm^3}$, and after substitution we determine the coefficient of volume expansion:

$\beta_{glass}=\frac{(4\,{ \cancel{{cm}^3}} )}{(10^4\,\cancel{{cm}^3})(15\,K)} \\ \implies \beta_{glass}=2.667\times 10^{-5}\,K^{-1}$

In conclusion, we find the coefficient of cubical expansion of glass to have the value $\beta_{glass}=2.667\times 10^{-5}\,{K}^{-1}$.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.