homework1solution

# homework1solution - MatSc503 Spring 2002 Solutions to...

This preview shows pages 1–2. Sign up to view the full content.

MatSc503 – Spring, 2002 Solutions to Homework #1 1) Hydrogen at 1.0 MPa is to be stored at 400 o C in outer space, in a thin wall (0.1 mm) spherical iron tank of 0.1 m radius. Please calculate the rate of pressure drop ( MPa/s ) as a result of diffusion of hydrogen through the wall. Take D = 10 -8 m 2 /s, and assume that the concentration of hydrogen in the iron at either side of the wall is the equilibrium solubility given by the equation c H ( p ) = 10 -5 p 1/2 gm H /gm Fe ( p in MPa ) ( gm – gram ) Solution: This is a quasi-steady state problem, i.e., the local concentration of H in the wall varies with time, but at any given moment of time, the total flux of H is a constant through the wall thickness, ( ) constant 1 4 4 2 = = = r d dc D dr dc D r J H π π Let’s use R 1 and R 2 to denote the inside and outside wall radii, and C 1 and C 2 the inside and outside wall concentrations, respectively, we have 2 1 1 2 2 1 1 2 1 2 4 1 1 4 R R C C DR R R C C D J H = π π From conservation of mass, we have dt dp RT V dt dn R R C C DR J H = = = 2 1 1 2 2 1 4 π where n is the total number of moles of H 2 in the tank, V is the volume of the tank, R is the gas constant, T is temperature, and p is the H 2 gas pressure which decreases slowly as a function of time. In the above equation, the ideal gas law is assumed for H 2 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern