Answer to Question #244041 in Atomic and Nuclear Physics for Michael

Question

1. A metal rod is cooled from 75 °C to –20 °C, and the length is held constant. The linear coefficient of thermal expansion of the metal is 17 × 10^–6 (°C)^–1, and its elastic modulus is 210 GPa. Determine the magnitude and type of stress developed during the cooling.              

1. To what temperature would 18.75 g of an iron specimen initially at 20 °C be raised if 1000 Joules of heat are supplied? (The specific heat capacity of iron is 0.46 J/g °C.)   

Answer 1

1) The relative change in length (contraction) is

$$\epsilon=\frac{L_0-L}{L_0}=\frac{L_0-L_0(1+\alpha\Delta T)}{L_0},\\\space\\ \epsilon=\frac{L_0-L_0(1+\alpha(-20-70))}{L_0}=1.53·10^{-3}.$$

The stress is

$$\sigma=E\epsilon=(210·10^9)(1.53·10^{-3})=321.3·10^6\text{ Pa}.$$

This is axial stress.

2) The equation for the heat supplied is

$$Q=cm(T_f-T_i),\\\space\\ T_f=\frac{Q}{cm}+T_i=\frac{1000}{460·0.01875}+20=136°\text C.$$