An external pressure P is applied on a cube at 00C so that it is equally compressed from all sides.  K is the bulk modulus of the material of the cube and \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 :

 

  • Option 1)

    \frac{P}{3\alpha K}

  • Option 2)

    \frac{P}{\alpha K}

  • Option 3)

    \frac{3\alpha }{PK}

  • Option 4)

    3PK\alpha

 

Answers (1)

As we learnt in

Liquid -

It is the type of matter which has got fixed volume but not fixed shape. Force of attraction between any two molecule is not that large as in case of solid . 

- wherein

e.g. Water, alcohol, milk etc.

 

 Bulk modulus is defined as 

K=-\frac{\Delta P}{\left(\frac{\Delta V}{V} \right )}=-\frac{P}{\left(\frac{\Delta V}{V} \right )}

\Delta V_{1}=-\frac{PV}{K}

Change in volume by heating 

\Delta V_{2}=V\gamma\Delta T=V.\left(3\alpha\Delta T \right )

\Delta V_{2}=3\alpha V\Delta T

Since net change in volume is zero.

\Rightarrow\ \; \Delta V_{1}+\Delta V_{2}=0

\Rightarrow\ \; -\frac{PV}{K}+3\alpha V\Delta T=0     or       \Delta T=\frac{P}{3\alpha K}

Correct option 1.


Option 1)

\frac{P}{3\alpha K}

This is the correct option.

Option 2)

\frac{P}{\alpha K}

This is an incorrect option.

Option 3)

\frac{3\alpha }{PK}

This is an incorrect option.

Option 4)

3PK\alpha

This is an incorrect option.

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