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Solution for The Pressure P and Volume V of a Gas Are Connected by the Relation Pv1/4 = Constant. the Percentage Increase in the Pressure Corresponding to a Deminition of 1/2 % in the Volume is (A) 1 2 % - CBSE (Commerce) Class 12 - Mathematics

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Question

The pressure P and volume V of a gas are connected by the relation PV1/4 = constant. The percentage increase in the pressure corresponding to a deminition of 1/2 % in the volume is

(a) \[\frac{1}{2} \%\]

(b) \[\frac{1}{4} \%\]

(c)  \[\frac{1}{8} \%\]

(d) none of these

Solution

(c) \[\frac{1} {8} \]%

We have

\[\frac{\bigtriangleup V}{V} = \frac{- 1}{2} % \]

\[P V^\frac{1}{4} = \text { constant  }= k \left( \text { say } \right)\]

\[\text { Taking log on both sides, we get }\]

\[\log \left( P V^\frac{1}{4} \right) = \log k\]

\[ \Rightarrow \log P + \frac{1}{4}\log V = \log k\]

\[\text { Differentiating both sides w . r . t . x, we get }\]

\[\frac{1}{P}\frac{dP}{dV} + \frac{1}{4V} = 0\]

\[ \Rightarrow \frac{dP}{P} = - \frac{dV}{4V} = - \frac{1}{4} \times \frac{- 1}{2} = \frac{1}{8}\]

\[\text { Hence, the increase in the pressure is } \frac{1}{8} \% .\]

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 9 | Page no. 13

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Solution for question: The Pressure P and Volume V of a Gas Are Connected by the Relation Pv1/4 = Constant. the Percentage Increase in the Pressure Corresponding to a Deminition of 1/2 % in the Volume is (A) 1 2 % concept: Approximations. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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