Question
For an ideal gas, how does the plot of $\log\text{p vs}\log\text{V}$ differ from that of $\text{V vs}\log\text{T}$? Explain.
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Answer
The plot of $\log \text{p vs}\log \text{V}$ is based on Boyle's law, whereas that of $\text{V vs} \log \text{T}$ is based on Charle's law.
Boyle's law
pV = k
Charle's law
$\frac{\text{V}}{\text{T}}=\text{k}$
$\begin{matrix}\log \text{p}+\log\text{V}=\log\text{k} & \log \text{V}-\log\text{T}=\log\text{k} \\\log\text{p}=-\log\text{V}+\log\text{k} & \log\text{V}=\log\text{T}+\log\text{k} \end{matrix}$
Both equations (i) and (ii) are comparable to y = mx + C and therefore, they represent straight lines. Their plots are as under.
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