L'Hospital's Rule

I found the L'Hospital's rule extremely useful when I was doing process control homework tonight. So if you are not familiar with it, or can't recall it clearly, here it is.

In words, if taking limit directly doesn't work out, one thing you can do is to take derivative of the numerator and the denominator at the same time. Then take limit. Remember, after this step, if the limit still doesn't work, you can apply the L'Hospital's rule again and again until you find a way that the limit can be taken.

This can be simply applied to the initial value theorem and final value theorem in process control.

                    Initial Value Theorem

                    Final Value Theorem

                                                   
                    where F(s) is the Laplace transformation of f(t).

Hope this will help someone who are looking for a way to solve the limit problems.

Raining (Steady State?)

So, it's raining heavily outside.

This morning, I got an email saying NYC will have tornado and thunderstorm. I called my mom immediately for regarding it, and told her not to go out today. Couple hours later, the rain came to Troy which is 160 miles north of NYC. These couples hours are the residence time for the rain travelling from NYC to Troy.

But, in the afternoon, I got another email from nyc.gov that eastbound of Grand Central Parkway closed due to severe flooding. Obviously, this whole system (the world) becomes non-steady state. In - Out != ZERO. Last summer, as I read news of Beijing flooding, the Forbidden City didn't have any negative effect. Even flooding in the city caused more than 50 people's deaths, the Forbidden City did not have any flooding, not at all. Are we smarter than our ancestors? More than 600 years of history, this old city is even better than our modern "civilization"? One reason can explain why. Modern technology "destroys" our environment. The effect will be the following: human beings, the modern inventors, will suffer from our great projects.

No Contradiction Between Protecting the Environment and Developing New Technology!

First Post

This is my first post in the blog. After doing all 4000 level chemical engineering homework together with Ken, Chris and Hisham, I think this blog will be interesting for people to share their chemical engineering experiences.

As usual, we were doing ChmE homework again in library. After spending almost 4 hours trying to solve one single problem, we found that the problem statement could be wrong. More ironically, when we did the same question yesterday, we found that the question was different in 2nd edition and 3rd edition textbook. With common sense, we followed the newer version. But, today we found that the 2nd edition was correct?

First lesson: 

Get the "real" book or you will regret.

Question:

Are the molecular sieves used in pressure-swing adsorption?

Since this is the first post of the blog, I do not want to make it so intense.