I do not see how such a process is possible, given that the volume of an ideal gas is supposed to depend solely upon its pressure and temperature. However, one of the problems I recently tried talked about the change in entropy of a system undergoing exactly such a process. What am I missing?
I think the process you are talking about is free expansion of ideal gas in vaccum.
Consider a cylinder mounted with piston, at t=0 it is put in vaccum and set into motion.
Now since the external pressure is zero, the gas expands freely. Here the process is isobaric since external pressure is const = zero. From what i know when we talk about the pressure of a process its generally the external pressure (against which work is being done) that is considered. But since in thermodynamics the polytropic processes are studied as being quasi static and reversible, the external and internal pressure remain in equlibrium and equal at all instant, and are used interchangeably in equations.
Now the internal pressure goes on varying with the volume such that PV remains constant and hence temp T remains constant. Thus its isothermal also.
Further the volume also keeps on increasing and hence its non isochoric in nature.
As a additional note, the entropy of this process( free expansion) is positive. Also this process is irreversible.
Your question can be generalized to any kind of system, not only pure gas but also multicomponent real systems, which have a fixed composition. For all these systems, imposing two variables such as pressure and temperature leads to unique values of all other system's properties, including its volume. Therefore, an isothermal (fixed temperature) and isobaric (fixed pressure) transformation of any system must keep its volume constant, making the transformation isochoric.