A metal rod has a length of 100.00 cm at the freezing point of water. A new temperature scale W is defined on which the freezing point of water is 20^ W and the boiling point of water is 170^ W . When the rod is heated to a temperature of 95^ W , its new length is found to be 100.10 cm . The coefficient of linear expansion of the metal in ^ C ⁻¹ is:

Step-by-step solution

First, we find the temperature of the rod on the Celsius scale when it is at 95^ W . The relationship between scale W and the Celsius scale is: t_W - 20 170 - 20 = t_C - 0 100 - 0 95 - 20 150 = t_C 100 75 150 = t_C 100 t_C = 50^ C The initial temperature of the rod is the freezing point of water, which is 0^ C . Therefore, the change in temperature is: t_C = 50^ C - 0^ C = 50^ C The change in length of the rod is: L = 100.10 cm - 100.00 cm = 0.10 cm Using the formula for linear expansion, L = L₀ t_C : 0.10 = 100.00