Question

A rod of iron and a rod of zinc are each 2 meters long at 0 degree and both are heated equally. At 50 degrees centigrade the Zinc rod is found to be longer by 0.181cm. Find the linear expansivity of iron when that of zinc is 0.0000598 per k.

Answer 1

$i_0 = z_0 = l_0 = 2~\text{m}; \\ (z_{50} - i_{50}) = 0.181~\text{cm} = 0.00181~\text{m}; \\ \alpha_z = 0.0000598~\text{K}^{-1}; \\ {\Delta}t = 50~\text{K}; \\ (z_{50} - i_{50}) = z_0(1+\alpha_z{\Delta}t) - i_0(1+\alpha_i{\Delta}t); \\ \alpha_i = \alpha_z - \frac{z_{50}-i_{50}}{l_0{\Delta}t} = 0.0000598~\text{K}^{-1} - \frac{0.00181~\text{m}}{2~\text{m}~*~50~\text{K}} \approx 0.0000417~\text{K}^{-1}.$