OUNT OF HEAT ABSORBED AND WORK DONE IN A PV DIAGRAM?

In summary, the problem involves a dilute gas with an initial pressure of 1.00 atm and a volume of 14.0 L, which is heated to a final state with a pressure of 2.00 atm and a volume of 78.0 L. The goal is to find the work done by the gas and the heat absorbed by the gas. To do so, the area under the PV curve must be calculated, which is not a triangle as previously thought. The units for volume must also be converted to match the units of the other quantities. Additionally, the relationship between work done, heat flow, and change in internal energy must be considered, and the change in temperature must be calculated to find the heat flow.
  • #1
paradiselost5
1
0

Homework Statement



One mole of a dilute gas initially has a pressure equal to 1.00 atm, and a volume equal to 14.0 L. As the gas is slowly heated, the plot of its state on a PV diagram moves in a straight line to the final state. The gas now has a pressure equal to 2.00 atm, and a volume equal to 78.0 L.

(a) Find the work done by the gas.


(b) Find the heat absorbed by the gas.

Homework Equations





The Attempt at a Solution


I took the area under the PV curve which is a triangle... 64/2*101.325
 
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  • #2
paradiselost5 said:


The Attempt at a Solution


I took the area under the PV curve which is a triangle... 64/2*101.325

Watch out: It is not a triangle. The work done by the gas is the area under the PV curve down to P=0.

ehild
 
  • #3
In addition to what ehild points out, watch the units for volume. If you are using MKS units you have to convert litres to _________.

What is the relationship between work done, heat flow and change in internal energy? To find the heat flow, what other quantity do you have to find? (hint: what is the change in temperature?).

AM
 

Related to OUNT OF HEAT ABSORBED AND WORK DONE IN A PV DIAGRAM?

1. What is a PV curve?

A PV (pressure-volume) curve is a graphical representation of the relationship between pressure and volume in a system. It is commonly used in thermodynamics to analyze the work done on a gas during a process.

2. How is work calculated from a PV curve?

The work done on a gas can be calculated by finding the area under the PV curve using the formula W = ∫PdV. This calculates the work done for a specific process or change in volume.

3. What does the shape of a PV curve indicate?

The shape of a PV curve indicates the type of process that is occurring. For example, a horizontal line indicates an isobaric process (constant pressure), while a vertical line indicates an isochoric process (constant volume).

4. Can a PV curve be used to determine the efficiency of a system?

Yes, a PV curve can be used to determine the efficiency of a system by comparing the work done on the gas to the heat added to the system. The efficiency can be calculated using the formula η = W/Q, where η is the efficiency, W is the work done, and Q is the heat added.

5. What are some real-world applications of PV curves?

PV curves have a variety of real-world applications, including in the design and analysis of heat engines, refrigeration systems, and gas turbines. They are also used in the study of atmospheric processes, such as weather patterns and climate change. Additionally, PV curves are used in the development of new materials and in the pharmaceutical industry for drug delivery systems.

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