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Q. Which of the following relation is correct?
(i) \(\frac{x}{m}=\) constant (at high pressure)
(ii) \(\frac{x}{m}=\) constant \(\times p^{1 / n}\) (at intermediate pressure)
(iii) \(\frac{x}{m}=\) constant \(\times p^{n}\) (at lower pressure)
A All are correct
B All are wrong
C. (i) and (ii) are correct
D (iii) is correct

4 Answers

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Solution:
At lower pressure, the graph is nearly straight and sloping, i.e.,
$$
\begin{aligned}
&\frac{x}{m} \propto p^{1} \\
&\text { or } \frac{x}{m}=\text { constant } \times p^{1}
\end{aligned}
$$
At high pressure, \(\frac{x}{m}\) becomes independent of value of pressure.
$$
\begin{aligned}
&\frac{x}{m} \propto p^{0} \\
&\text { or } \frac{x}{m}=\text { constant }
\end{aligned}
$$
In the intermediate range of pressure, \(\frac{x}{m}\) will depend on \(p\) raised to powers between 1 and 0 , i.e., fractions.
$$
\begin{aligned}
&\frac{x}{m} \propto p^{\frac{1}{n}} \\
&\text { or } \frac{x}{m}=\text { constant } \times p^{\frac{1}{n}}
\end{aligned}
$$
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