Consider a cylinder with a moveable piston. Cylinder is not thermally insulated from the environment. Initially inside of the cylinder is saturated water vapor at the pressure of 20 bar. Imagine that at some point this cylinder is placed into a thermal contact with a large reservoir with a constant temperature of 180 ◦C. a) After cylinder reaches thermal equilibrium with the reservoir, what is the final state of the water in the cylinder? Is it a compressed liquid, saturated liquid, mixture, saturated vapor, or superheated vapor? Briefly explain. b) Is the heat during this process taking energy from the water to the reservoir, or the other way around? Briefly explain. c) Is this a reversible process or an irreversible process? Briefly explain.
The Correct Answer and Explanation is:
a) Final state of the water in the cylinder:
When the cylinder reaches thermal equilibrium with the reservoir at a constant temperature of 180°C, the water in the cylinder will adjust according to the saturation properties of water at this temperature.
At 180°C, the saturation pressure of water is approximately 18.54 bar, which is lower than the initial pressure of 20 bar inside the cylinder. The initial state of the water was saturated vapor at 20 bar, which corresponds to a pressure higher than the saturation pressure at 180°C.
- As the cylinder is placed in thermal contact with the reservoir, the temperature increases, and the water inside the cylinder will eventually reach 180°C.
- Since the pressure of 20 bar is greater than the saturation pressure at 180°C (18.54 bar), the water will be forced into a superheated vapor state, where the vapor is at a temperature higher than the saturation temperature for that pressure.
Thus, the final state of the water in the cylinder will be superheated vapor at 180°C and a pressure of 20 bar.
b) Direction of heat flow:
The heat flow during this process will be from the reservoir to the water.
- Initially, the cylinder contains saturated vapor at 20 bar, which is at a higher temperature than 180°C, since at 20 bar the corresponding saturation temperature would be much higher (around 212°C).
- As the cylinder reaches thermal equilibrium with the reservoir at 180°C, heat must flow from the thermal reservoir into the water to cool it down and adjust the water’s properties to the new temperature.
- Since the water is initially at a higher temperature and the thermal reservoir is at 180°C, the heat flows from the reservoir to the water.
c) Reversibility of the process:
This process is irreversible.
- Irreversibility comes from the fact that there is a temperature difference between the water inside the cylinder and the thermal reservoir, which leads to a spontaneous heat transfer from the reservoir to the water. The temperature difference causes an increase in entropy, and the process cannot be reversed without external work or additional steps to return the system to its initial state.
- Additionally, the process involves the expansion or compression of the water’s phase, which is typically irreversible unless it occurs in a highly controlled manner (e.g., infinitely slow, without any dissipative losses). Since the cylinder is not insulated and there’s a direct heat transfer between the water and the environment, this further emphasizes the irreversibility of the process.
In conclusion:
- The final state is superheated vapor.
- Heat flows from the reservoir to the water.
- The process is irreversible due to the temperature gradient and the phase change dynamics.
