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JEE Main 20172 April
Exam
JEE Main
Year
2017
Date
2 April
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2017 · 2 April · Physics · Thermal Properties of Matter

An external pressure P is applied on a cube at 0 ° C so that it is...

An external pressure PP is applied on a cube at 0°C0 ° C so that it is equally compressed from all sides. KK is the bulk modulus of the material of the cube and α\alpha is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

Options

  1. A3PKα3PK\alpha
  2. BP3\alphaK\dfrac{P}{3\alphaK}
  3. CP\alphaK\dfrac{P}{\alphaK}
  4. D3αPK\dfrac{3\alpha}{PK}

Correct answer

B. P3\alphaK\dfrac{P}{3\alphaK}

Step-by-step solution

B=−P(dVV)B = \dfrac{- P}{\left(\dfrac{dV}{V}\right)}

dVV=−PB\dfrac{dV}{V} = \dfrac{- P}{B}

dV=−PVBdV = \dfrac{- PV}{B}

\DeltaV=Vγ\DeltaT\DeltaVV=γ\DeltaT\DeltaV = V\gamma\DeltaT\dfrac{\DeltaV}{V} = \gamma\DeltaT

\DeltaVV=3α\DeltaT\dfrac{\DeltaV}{V} = 3\alpha\DeltaT

K=P\DeltaVV=P3α\DeltaTK = \dfrac{P}{\dfrac{\DeltaV}{V}} = \dfrac{P}{3\alpha\DeltaT}

\DeltaT=P3\alphak\DeltaT = \dfrac{P}{3\alphak}
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