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 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)


  • Option 2)


  • Option 3)


  • Option 4)



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)


This is the correct option.

Option 2)


This is an incorrect option.

Option 3)


This is an incorrect option.

Option 4)


This is an incorrect option.

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