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JEE Main 202313 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
13 April
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2023 · 13 April · Morning Shift · Physics · Mechanical Properties of Solids

Under isothermal condition, the pressure of a gas is given by P = a...

Under isothermal condition, the pressure of a gas is given by P=aV–3,P = a{V}^{– 3}, where aa is a constant and VV is the volume of the gas. The bulk modulus at constant temperature is equal to

Options

  1. A3P3P
  2. BPP
  3. C2P2P
  4. DP2\dfrac{P}{2}

Correct answer

A. 3P3P

Step-by-step solution

The data given is

P=aV−3P = a{V}^{- 3}

Bulk modulus is given by,

B=−dPdVV=−VdPdVB = - \dfrac{dP}{\dfrac{dV}{V}} = - V\dfrac{dP}{dV}

=−VddV{aV3}= - V\dfrac{d}{dV}\left\{\dfrac{a}{{V}^{3}}\right\}

=−V[−3aV4]= - V\left[\dfrac{- 3a}{{V}^{4}}\right]

=3aV3=3P= \dfrac{3a}{{V}^{3}} = 3P

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