Learning Goal: To understand the meaning and the basic applications of pV diagra

Question

Learning Goal:

To understand the meaning and the basic applications of pV diagrams for an ideal gas.

As you know, the parameters of an ideal gas are described by the equation

pV=nRT,

where p is the pressure of the gas, V is the volume of the gas, n is the number of moles, R is the universal gas constant, and T is the absolute temperature of the gas. It follows that, for a portion of an ideal gas,

pVT=constant.

One can see that, if the amount of gas remains constant, it is impossible to change just oneparameter of the gas: At least one more parameter would also change. For instance, if the pressure of the gas is changed, we can be sure that either the volume or the temperature of the gas (or, maybe, both!) would also change.

To explore these changes, it is often convenient to draw a graph showing one parameter as a function of the other. Although there are many choices of axes, the most common one is a plot of pressure as a function of volume: a pV diagram.

In this problem, you will be asked a series of questions related to different processes shown on apV diagram (Figure 1) . They will help you become familiar with such diagrams and to understand what information may be obtained from them

Calculate the work W done by the gas during process 12631.

Express your answer in terms of p0 and V0.

4p0V0

W=

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4p0V0

Explanation / Answer

in General in PV diagram

the Work done in PV diagram is W = area under the curve

W = 0.5*b*h = 0.5*(3Vo-Vo)*(3Po-Po) = 0.5*2Vo*2Po = 2*Po*Vo

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