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

Question #244041
  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.)   
1
Expert's answer
2021-09-30T10:20:46-0400

1) The relative change in length (contraction) is


ϵ=L0LL0=L0L0(1+αΔT)L0, ϵ=L0L0(1+α(2070))L0=1.53103.\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


σ=Eϵ=(210109)(1.53103)=321.3106 Pa.\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(TfTi), Tf=Qcm+Ti=10004600.01875+20=136°C.Q=cm(T_f-T_i),\\\space\\ T_f=\frac{Q}{cm}+T_i=\frac{1000}{460·0.01875}+20=136°\text C.


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