N moles of a diatomic gas in a cylinder are at a temperature T.  Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas.  What is the change in the total kinetic energy of the gas ?

 

  • Option 1)

    \frac{1}{2}nRT  

  • Option 2)

    0

  • Option 3)

      \frac{3}{2}nRT

  • Option 4)

     \frac{5}{2}nRT

 

Answers (1)

As we learnt in

Specific heat of gas at constant volume -

C_{v}= \frac{fR}{2}

- wherein

f = degree of freedom

R= Universal gas constant

 

 Number of moles of diatomic gas = N 

Hence, Number of moles of monoatomic gas = 2N

Since T = constant and volume is also constant 

Work done = 0 

Change in internal energy = Heat supplied

Change in total kinetic energy = nfCvfT - niCviT

ni = N,     C_{vi}=\frac{5R}{2}

nf = 2N,     C_{vf}=\frac{3R}{2}

\therefore\ \; \Delta K=3NRT-\frac{5}{2}NRT=\frac{1}{2}NRT

Correct option is 1.


Option 1)

\frac{1}{2}nRT  

This is the correct option.

Option 2)

0

This is an incorrect option.

Option 3)

  \frac{3}{2}nRT

This is an incorrect option.

Option 4)

 \frac{5}{2}nRT

This is an incorrect option.

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