A piston/cylinder setup (Fig. P4.68) contains 1 kg of water at 20^∘ C with a volume of 0.1 m^3 .

step 1 Here in this question A, in part A, state to reach lift pressure of P, which is 400 kilopascal,

A piston/cylinder setup (Fig. P4.68) contains 1 kg of water...

A piston/cylinder setup (Fig. P4.68) contains 1 kg of water at $20^{\circ} \mathrm{C}$ with a volume of $0.1 \mathrm{m}^{3} .$ Initially, the piston rests on some stops with the top surface open to the atmosphere, $P_{0},$ and a mass such that a water pressure of $400 \mathrm{kPa}$ will lift it. To what temperature should the water be heated to lift the piston? If it is heated to saturated yapor, find the final temperature, volume, and work,

Key Concepts

Piston?Cylinder Systems and Boundary Work

This concept involves understanding that in a piston-cylinder device, any movement of the piston due to pressure changes results in work being done by or on the system. Analysis of these systems often requires applying the principles of work and energy transfer, where work is calculated as the product of pressure and the change in volume during a process. This is fundamental in designing and analyzing thermodynamic processes that involve moving boundaries.

Phase Change and Vapor–Liquid Equilibrium

Phase change refers to the transformation between different states of matter, such as liquid to vapor. In thermodynamics, the vapor–liquid equilibrium describes the condition under which the liquid and its vapor coexist at a given temperature and pressure. This concept is crucial when analyzing heating processes where a substance may reach a saturated state, meaning any additional heat can cause further phase change rather than a rise in temperature.

Thermodynamic Properties and Saturation Conditions

Understanding the properties of substances like water—such as specific volume, pressure, and temperature—is essential in thermodynamic analysis. Saturation conditions, determined from steam tables or property charts, indicate the temperature and pressure at which a substance is on the verge of phase change. These properties help in quantifying the state of the substance, whether it remains a compressed liquid, becomes a mixture, or turns into saturated vapor.

Pressure–Temperature Relationship in Saturated Systems

This concept focuses on the intrinsic relationship between pressure and temperature in a system undergoing a phase change. In a saturated system, the boiling point of a liquid is directly related to the pressure exerted on it. This relationship is key when designing processes where achieving or maintaining a certain pressure is required for the phase transition, such as in piston-cylinder setups where the lifting of a piston is directly linked to reaching a specific saturation pressure.

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