Question

Two gaseous systems in a cylinder are separated by a frictionless movable piston. The cylinder and piston are diathermal. Which of the following statements are true?

The systems are in equilibrium with respect to pressure only.

The systems are in equilibrium with respect to temperature only.

The systems are in equilibrium with respect to pressure and temperature.

The systems are in equilibrium with respect to pressure, temperature and composition.

Answer 1

Equilibrium in thermodynamics appears in the context where we say the state of a system is an equilibrium state if the macroscopic variables that characterise the system do not change in time. For example, a gas trapped inside a closed rigid container, insulated from its surroundings by means of an adiabatic wall, with fixed values of pressure, volume, temperature, mass and composition that do not change with time, is in a state of thermodynamic equilibrium.

Accprding to the question,

the Gaseous systems in a cylinder are seperated by a frictionless diathermic wall – a conducting wall that allows energy flow (heat) from one to another. Then the macroscopic variables of the systems A and B change spontaneously until both the systems attain equilibrium states. After that there is no change in their states. The pressure and volume variables of the two gases change such that the new states of A and B are in equilibrium with each other. There is no more energy flow from one to another. We then say that the system A is in thermal equilibrium with the system B. If the adiabatc wall is placed in between the gases then the pressure and the composition or the volume would have been in equilibrium.

Hence the Systems are in equilibrium with respect to the temperature only. The other macroscopic variables of the system will change