Reading a P-V Diagram for heat in/out and work in/out

In summary, when analyzing a P-V diagram, adiabatic steps moving from left to right and downward indicate 0 heat flow and positive work done by the gas, while steps moving from right to left and upward indicate 0 heat flow and negative work done on the gas by the surroundings. Isovolumic steps moving from bottom to top show heat flow into the gas and no work done, while steps moving from top to bottom show heat flow out of the gas and no work done. Isobaric steps moving from left to right show heat flow into the gas and positive work done by the gas, while steps moving from right to left show heat flow out of the gas and negative work done on the gas by the surroundings.
  • #1
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Homework Statement


Predict whether heat is lost or gained by a gas, and whether work is done by the gas or the gas does work on its surroundings, given a P-V diagram.


Homework Equations





The Attempt at a Solution



I'm trying to understand how to read a P-V diagram and am wondering whether there are any shortcut ways of determining whether heat has been added to the gas (which I think is positive Q) or left the gas (which I think is negative Q), and whether the gas has done work (positive) or had work done to it (negative). Is it ok to say the following?

Adiabatic steps moving from left to right and downward on the diagram: 0 heat change and gas does (positive) work.

Adiabatic steps moving from right to left and upward on the diagram: 0 heat change and environment does work on gas (negative work).

Isovolumic step moving from bottom to top on the diagram: heat added to the gas (positive Q) and 0 W

Isovolumic step moving from top to bottom on the diagram: heat taken from the gas (negative Q) and 0 W

Isobaric step moving from left to right on the diagram: heat added to the gas (positive Q) and the gas does (positive) work.

Isobaric step moving from right to left on the diagram: heat taken from the gas (negative Q) and the environment does work on the gas (work is negative)

Isothermal step moving from left to right and downward on the diagram: heat added to the gas (negative Q) and the gas does (positive) work.

Isothermal step moving from right to left and upward on the diagram: heat taken from the gas (negative Q) and the gas does (negative) work.
 
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  • #2
Pretty good. I would make the following changes (in bold):

Adiabatic steps moving from left to right and downward on the diagram: 0 heat flow and gas does (positive) work: W = ΔU

Adiabatic steps moving from right to left and upward on the diagram: 0 heat flow and environment does work on gas (negative work):W = ΔU

Isovolumic step moving from bottom to top on the diagram: heat flow into the gas (positive Q) and 0 W: Q = ΔU

Isovolumic step moving from top to bottom on the diagram: heat flow out of the gas (negative Q) and 0 W: Q = ΔU

Isobaric step moving from left to right on the diagram: heat flow into the gas (positive Q) and the gas does (positive) work.

Isobaric step moving from right to left on the diagram: heat flow out of the gas (negative Q) and the environment does work on the gas (work is negative)

Isothermal step moving from left to right and downward on the diagram: heat flow into the gas (negative Q) and the gas does (positive) work: Q = W

Isothermal step moving from right to left and upward on the diagram: heat flow out of the gas (negative Q) and the gas does (negative) work: Q = W

AM
 

1. What is a P-V diagram and how is it used to represent heat and work?

A P-V (pressure-volume) diagram is a graphical representation of the relationship between pressure and volume in a thermodynamic system. It is commonly used to visualize the transfer of heat and work in a system. The area under the curve on a P-V diagram represents the work done by the system, while the slope of the curve represents the pressure. Heat transfer is shown as a change in the temperature or volume of the system.

2. How can you determine the direction of heat and work on a P-V diagram?

The direction of heat and work can be determined by the direction of the curve on the P-V diagram. If the curve is in the positive direction, the heat or work is being added to the system. If the curve is in the negative direction, the heat or work is being removed from the system.

3. What is the relationship between heat and work on a P-V diagram?

The relationship between heat and work on a P-V diagram is represented by the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This can be seen on a P-V diagram as the area enclosed by the curve, which represents the change in internal energy.

4. Can you determine the efficiency of a system from a P-V diagram?

Yes, the efficiency of a system can be determined from a P-V diagram by calculating the ratio of the work output to the heat input. This is known as the thermal efficiency and is an important factor in evaluating the performance of a thermodynamic system.

5. How do you interpret a P-V diagram for a cyclic process?

For a cyclic process, the starting and ending points on the P-V diagram will be the same, as the system has returned to its original state. The area enclosed by the curve represents the net work done by the system during one cycle. The direction of the curve can also indicate the direction of the heat transfer during the cycle.

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