Meaning of 'constant T and p'
As a chemical engineer, my perspective on this differs from those of the other responders.  I regard a process occurring at constant temperature and pressure as one in which

The system is held in contact with a constant temperature over the portion of its interface with the surrounding through which heat transfer is occurring, not necessarily the initial temperature of the system, throughout the process

The external pressure (or more precisely, the external compressive stress) at the portion of the system interface with its surroundings at which displacement work is being done is held constant (not necessarily at the initial pressure of the system) throughout the process.