In a quasi-equilibrium process involving a system: a) The pressure remains constant. b) The pressure varies with temperature. c) The pressure is constant at an instant at each point in the system. d) The pressure force results in a positive work input.

In a quasi-equilibrium process, every intermediate step is infinitesimally close to equilibrium. However, this does not mean that the pressure must remain constant throughout the process. The pressure may change during the process, but it would do so slowly, allowing the system to adjust without moving too far from equilibrium. Therefore, statement (a) is false.

In general, pressure can vary with temperature in any process, including a quasi-equilibrium process. In fact, most processes will see a correlation between pressure and temperature, according to the ideal gas law: PV=nRT, where P is pressure, V is volume, n is the amount of substance, R is the universal gas constant, and T is temperature. As long as the quasi-equilibrium condition is met (i.e., the system is close to equilibrium at every step), the pressure can change with temperature. Therefore, statement (b) is true.

A key feature of a quasi-equilibrium process is that at any instant, the system is very close to equilibrium. This implies that pressure is uniform throughout the system at any given instant. As the process progresses, the pressure across the system may change, but at any instant, it remains constant throughout the system. Therefore, statement (c) is true.

In a quasi-equilibrium process, work can be done on or by the system. The work done by or on a system depends on the process and the sign convention used. In general, if the system is expanding, the work done on the surroundings is considered positive and the work done on the system is considered negative because the pressure force needs to overcome the external force. If the system is being compressed, the work done on the system is considered positive, while work done by the system on the surroundings is considered negative. Therefore, statement (d) may not always be true. The pressure force may result in positive work input, but it can also result in negative work input depending on the particular process being performed.