What is the difference between in work and at work? Does in work imply that the person is busy and immersed in his work?
I am at work.
He is in work.
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I upvoted a comment yesterday that I believe is worthy of repeating:
Prepositions are notoriously fickle in how they're paired with verbs (in many languages, not just English).
Indeed, in work can mean exactly what you said:
The designers were so immersed in work that they didn't even notice they had toiled through their lunch hour.
But in work can be used in many other contexts as well:
“Involvement in work has brought major changes in the lifestyle of several of our respondents.” (L. Gulati)
“Contentment in work is likewise necessary for a sense of individual well-being.” (Lifchez & Winslow)
“To some extent, each individual defines self in terms of what that individual does in work.” (Gould & Smith)
“Equally, some of those people who are in work look enviously at those who are not in work.” (House of Commons Parliament debate, 1985)
At work is similar, in that there are several possible nuances:
He stayed at work until seven o'clock.1
There are men at work on the roadside.
People have a higher risk of injury at work than at home.
The designers were so engaged at work that they didn't even notice they had toiled through their lunch hour.
1Interestingly enough, this one could mean "He stayed working until 7:00" or "He stayed at his place of employment until 7:00."
An American would be very unlikely to say, "He's in work."
"He is at work" usually means he is presently at his place of employment. It can also mean he is presently engaged in work. Like if someone is at home but doing something related to his job, and an interruption comes along, he might say, "I'm at work -- tell them to call back later".
I can't think of a general rule or pattern for when you would use "in work". It is almost always used with a verb like "engaged" and some sort of descriptive phrase to describe the work. Like, "He is engaged in dangerous work", or "He is tied up in work that is very tedious and boring."
from the Longman Language Activator:
be in work [British]: to have a job - use this when you are comparing someone who has a job with other people who do not have jobs
She was the only one in the family to be in work.
be at work: to be doing your job at the place you work, especially at a factory, office etc owned by your employer
What time do you have to be at work?
As you can see, "to be in work" is not a common idiom in American English.