Understanding Positive and Negative Work in Closed PV Graphs

• Jayhawk1
In summary, a closed PV graph is a visual representation of the relationship between pressure and volume in a closed system. The work done in the system can be determined by calculating the area under the curve on the graph. If the system expands, positive work is done, while if it contracts, negative work is done. For a closed loop, the work done can be determined by the direction of the loop, with clockwise indicating positive work and counterclockwise indicating negative work.
Jayhawk1
Can someone please breifly explain to me how a closed PV graph works? ...In particular how to determine whether positive or negative work had been done within the system?

By convention, a system that expands (smaller volume -> bigger volume) does positive work.

In a PV diagram the work done equals the area under the curve of P vs V. so if the system starts at a smaller V and goes to a larger V the work just equals the area under the graph (and area is always positive ). If the system does the reverse and goes from larger volume to smaller volume, then the work equals the negative of the area under the graph.

For a closed loop, the work done equals the area enclosed by the loop. You determine whether its positive or negative based on the direction. Clockwise gives positive work, and counter clockwise gives negative work.

What is a PV graph?

A PV graph, also known as a pressure-volume graph, is a visual representation of the relationship between pressure and volume in a system. It is commonly used in thermodynamics to analyze the behavior of gases.

How is a PV graph used in thermodynamics?

In thermodynamics, a PV graph is used to analyze the changes in pressure and volume of a gas as it undergoes different processes, such as isothermal, adiabatic, and isobaric processes. It helps to understand the work, heat, and energy transfers that occur within a system.

What is the significance of the shape of a PV graph?

The shape of a PV graph can provide important information about the behavior of a gas. For example, a horizontal line indicates a constant pressure, while a vertical line indicates a constant volume. The slope of the line can also indicate the magnitude and direction of work done on or by the system.

Can a PV graph be used to determine the state of a gas?

Yes, a PV graph can be used to determine the state of a gas by identifying the point at which the system is at equilibrium. This point is known as the intersection of the two curves on the graph, and it represents the state variables of the gas (pressure, volume, and temperature) at that specific moment.

What are some real-world applications of PV graphs in thermodynamics?

PV graphs have numerous real-world applications in thermodynamics, including the design of engines, refrigeration systems, and heat pumps. They are also used in the study of weather patterns, ocean currents, and other natural phenomena where gas behavior plays a significant role.

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