A piston/cylinder contains 1 kg of water at 20^∘ C with volume 0.1 m^3 . By mistake someone lock

step 1 For this problem on the topic of work and heat, we are told that a piston cylinder device contai

A piston/cylinder contains 1 kg of water at 20^∘ C with...

A piston/cylinder contains 1 kg of water at $20^{\circ} \mathrm{C}$ with volume $0.1 \mathrm{m}^{3} .$ By mistake someone locks the piston, preventing it from moving while we heat the water to saturated vapor. Find the final temperature and volume, and the process work.

Key Concepts

Process Work in Thermodynamic Systems

Process work refers to the work done by or on the system during a thermodynamic process. In the context of a constant volume process, even though energy may be added in the form of heat, no boundary work is performed because the volume does not change. This concept is important when calculating the work output (or input) of the process, which in such cases is zero.

Thermodynamic Properties of Water

Understanding and using the thermodynamic properties of water from steam tables (or equations of state) is crucial for analyzing problems involving heating and phase change. These properties, such as the specific volumes for the saturated liquid and vapor at different temperatures, help in predicting the final state of the water when it is heated under constant volume conditions.

Saturated Vapor and Phase Change

The notion of saturated vapor refers to the condition where a substance is at the temperature and pressure at which it can coexist in equilibrium between the liquid and vapor phases. When a substance is heated until it becomes saturated vapor at a particular specific volume, its temperature adjusts such that the vapor phase exactly fills that specific volume at saturation conditions. This concept is essential in determining the final state in processes involving phase change.

Constant Volume Process

A constant volume (isochoric) process implies that the volume of the system remains fixed throughout the process. In thermodynamics, heating or cooling a substance at constant volume means that the work done by or on the system is zero since work is generally defined by a change in volume under pressure. This concept is fundamental when analyzing processes in a piston/cylinder arrangement where the piston is locked.

Specific Volume

Specific volume is defined as the volume per unit mass of a substance and is a key intensive property in thermodynamics. It is used to characterize the state of a substance, especially during phase change processes where the specific volume of saturated liquid (v_f) and saturated vapor (v_g) vastly differ. Matching the system's specific volume to the property values in steam tables allows one to determine the state (temperature, pressure) of the substance.

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