If pv-81- then dp-dv at v-9 is equal to

Finding the derivative:Given that, pv=81.To evaluate dp/dvconsider pas constant amp; differentiate pv=81.p=81/vDifferentiating with respect to v both sides w ...

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Byju's Answer

Standard XII

Chemistry

Liquefaction of Gases and Critical Constants

If pv=81, the...

Question

If $p v = 81$ , then $\frac{d p}{d v}$ at $v = 9$ is equal to

$1$

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$2$

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None of these

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Solution

The correct option is B
$- 1$

Finding the derivative:
Given that, $p v = 81$ .
To evaluate $\frac{d p}{d v}$ consider $p$ as constant & differentiate $p v = 81$ .
$p = \frac{81}{v}$
Differentiating with respect to $v$ both sides we have:
$\frac{d p}{d v} = - \frac{81}{v^{2}}$
At, $v = 9$ .
$\begin{array}{rcl} \frac{d p}{d v} & = & - \frac{81}{9^{2}} \\ = & - \frac{81}{81} \\ = & - 1 \end{array}$
Hence, option (B) is correct.

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If pv=81, then dpdv at v=9 is equal to

The correct option is B -1Finding the derivative:Given that, pv=81.To evaluate dpdvconsider pas constant & differentiate pv=81.p=81vDifferentiating with respect to v both sides we have:dpdv=-81v2At, v=9.dpdv=-8192=-8181=-1Hence, option (B) is correct.

If $p v = 81$ , then $\frac{d p}{d v}$ at $v = 9$ is equal to