Using equipartition of energy, the specific heat (in J kg-1 K-1) of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27)

 

  • Option 1)

     25
     

     

  • Option 2)

    410

  • Option 3)

    925

     

  • Option 4)

    1850

 

Answers (1)

As we learnt in

Kinetic energy of a gas due to translation per mole -

E= \frac{3}{2}PV

= \frac{3}{2}RT
 

- wherein

R = Universal gas constant

T = temperature of gas

 

 Using equipartition theorem. 

Energy associated with each degree of freedom =\frac{1}{2}RT =\frac{1}{2}RT\ per\ mole

For solid  V = 3KT = mcT.

c=\frac{3\times1.38\times 10^{-23}}{ \left(\frac{27\times10^{-3}}{6.023\times10^{23}} \right )}   [Mass of 6\times 10^{-23} molecule of Aluminium 27\times 10^{-23}kg]

c = 925 J/kg-K

Correct option is 3.


Option 1)

 25
 

 

This is an incorrect option.

Option 2)

410

This is an incorrect option.

Option 3)

925

 

This the correct option.

Option 4)

1850

This is an incorrect option.

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