Question

A rectangular blockof volume 10^-3 at 273k is heated to 573k.If it's coefficient of linear expansion is 1.2*10^-5k^-1.the percentage change of it's volume is

Answer 1

The new volume is

$$V_1=a_1b_1c_1,\\ V_1=[a(1+\alpha\Delta T][b(1+\alpha\Delta T)][c(1+\alpha\Delta T)],\\ V_1=abc(1+\alpha\Delta T)^3.$$

The percentage change of the volume is

$$\epsilon=\frac{V_1-V}{V}·100\%,\\\space\\ \epsilon=[(1+\alpha\Delta T)^3-1]·100\%=1.08\%.$$