The pressure on a sample of water is increased from 1 atm to...

The pressure on a sample of water is increased from 1 atm to 200 atm, reducing its volume by $1 \%$. (a) Draw the pressureversus-volume graph for this process. (b) Estimate the work required. (c) Assume that the process takes place quickly enough so that no heat flows out of the water. By how much does the water's temperature increase?

Key Concepts

Pressure-Volume Diagrams

A pressure?volume diagram is used in thermodynamics to graphically represent the relationship between pressure and volume during a process. In such a diagram, different processes (like compression or expansion) are shown as curves whose shapes reveal how pressure changes with volume. The area under the process curve corresponds to the work done by or on the system, making these diagrams essential for visualizing and calculating thermodynamic work.

Thermodynamic Work

In thermodynamics, work is defined as the energy transfer occurring when a force moves a boundary. Specifically, for processes involving volume change, the work done is given by the integral of pressure with respect to volume (W = ? P dV). When pressure is not constant, one must account for its variation with volume, and the work performed is represented by the area under the pressure–volume curve on the graph.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged between the system and its surroundings. This means that any work done on or by the system directly alters its internal energy, which typically results in a change in temperature. Adiabatic assumptions are particularly useful when the process happens rapidly, allowing no time for significant heat transfer.

Temperature Change Due to Compression

When a system is compressed adiabatically, the mechanical work done on the system increases its internal energy, leading to a rise in its temperature. The increase in temperature can be estimated by relating the work done to the system's heat capacity. This concept illustrates the conversion of work into thermal energy and is a fundamental aspect of adiabatic processes in thermodynamics.

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