Question

A Zinc rod is measured by means of a brass scale (which is correct at 0 degree) and is found to be 1.0001 metres long at 10 degrees. What is the real length of the rod at 0 degree and at 10 degrees? Mean linear expansivity of the Zinc and is 0.000029 per K and of brass is 0.000019 per K.

Answer 1

$z_{10} = z_0(1+\alpha_z{\Delta}t) = b_{10} = b_0(1+\alpha_b{\Delta}t); \\ b_0 = 1.0001~\text{m}; \\ z_0 = b_0\frac{1+\alpha_b{\Delta}t}{1+\alpha_z{\Delta}t} = 1.0001~\text{m}~\frac{1+0.000019~\frac{1}{{\text{K}}}10~{\text{K}}}{1+0.000029~\frac{1}{{\text{K}}}10~{\text{K}}} \approx 1.00008999929~\text{m}; \\ z_{10} = b_0(1+\alpha_b{\Delta}t) = 1.0001~\text{m}~(1+0.000019~\frac{1}{{\text{K}}}10~{\text{K}}) \approx 1.0001190019~\text{m}.$