Question

A change in the process requires a higher temperature. The temperature of the pipe increases from T-800 K to T2 900 K. Now, the flux will change because diffusion will be easier at higher temperatures. This will cause the value of D in Fick's First Law to increase. Assume that the activation energy for the diffusion of hydrogen through the pipe is Ed 1.51x104 J/mol. What is the leak rate for the new process? Express your answer to three significant figures with the appropriate units View Available Hint(s) IA Value Units

Answer 1

$Given\ that\\ T_1=800 ,T_2=900 K\\ E_d=1.51\times10^4\ J/mol\\ We\ know\ that\\ ln\frac{R_2}{R_1}=\dfrac{E_d}{R}\left ( \dfrac{1}{T_1}-\dfrac{1}{T_2} \right )\\ Where,R_1\ and\ R_2\ are\ leak\ rate\\$

$ln\frac{R_2}{R_1}=\dfrac{1.51\times10^4}{8.314}\left ( \dfrac{1}{800}-\dfrac{1}{900} \right )\\ \ln\dfrac{R_2}{R_1}=0.25225$

$R_2=1.286R_1\\$

Therefore new rate of leak

$\Delta R=\dfrac{R_2-R_1}{R_1}\times 100\\ \Delta R=\dfrac{1.286R_1-R_1}{R_1}\times 100\\ \Delta R=28.6\ percent$

Therefore the new leak rate will increase by approximately 30 %.