I have completed my Bachelors of Engineering and I now want to purse my PhD in Computer Science. I have written essays for my Masters application before and I am familiar with the context of those essays. How different are they from PhD application essays? And how should I proceed with writing my PhD application essay?
First, I would recommend reading some of the requirements from schools you intend on applying to. Most schools have very similar requirements, but it may be worth looking at the schools that you are most interested in attending before you get started (page requirements, etc. can deviate from school to school).
Since you are applying to PhD programs you will want to be addressing the questions of "What makes you an individual well suited to research in computer science?" and "Why should institution X accept you?"-- this will involve talking about your past achievements, what made you want to pursue a PhD in computer science, what type of research you want to do, etc.
As far as definitive strategy goes, there are numerous routes you can go (I will leave a couple of links at the end of this post). One that I would recommend is to write the majority of the statement such that it can be sent to any institution (i.e., is not institution specific). Set it up (as far as continuity goes) so that your last paragraph is why you want to attend institution X. This way you will only need to re-write the last paragraph for each application you send out.
Here are some helpful links I found:
Hope that helps!