I guess you are enquiring about the research culture of IIT Kharagpur rather than the life of a Ph.D. student as his/her life is based on research only. 

• A typical Ph.D. student is always invested in some or other research work like INDEST, SCOPUS, and Publications.
• The research work depends largely on the particular department and the faculty advisor.
• Each research student is given a research problem on which he works and submits good-quality publications after which his Ph.D. is given.
• Some students are given the opportunity to explore and choose a research topic on their own. These students are guided by friendly faculty advisors who are not only excellent in their field but also guide you throughout the journey.
• Usually it takes more than 4 years to obtain a Ph.D. in a Science or Social Science department whereas less than 4 years in an Engineering department.

It is not necessary to be confined within the walls of your department lab as a Ph.D. student. Some choose the relaxed way and enjoy their campus life to the fullest as well.