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Longest Chain Rule

Draw the pres...

Question

Draw the pressure-temperature and volume-temperature diagrams for an isobaric process of expansion, corresponding to $n$ moles of an ideal gas at a pressure $P_{0}$ , from $V_{0}$ to $2 V_{0}$ .

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Solution

From the equation state for an ideal gas $P V = n R T$ ,
We have $V = (\frac{n R}{P_{0}}) T$ or $V α T$
At $V = V_{0}$ , we get $T_{1} = \frac{P_{0} V_{0}}{n R}$
And at $V = 2 V_{0}$ , we get
$T_{2} = \frac{2 P_{0} V_{0}}{n R}$
For the graph of $P$ versus $T$ the variation is a straight line normal to the pressure axis, the temperature varies from $T_{1}$ to $T_{2}$ as shown in the figure.
For the graph of $V$ versus $T$ , the equation $V = (\frac{n R}{P_{0}}) T$ or $V = k T$ shows that the volume varies directly with the temperature (Charlie's law). So, the graph is a straight line inclined to the (V-T) axes, and passes through the origin (when produced) as shown in figure.

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