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  • A gas consisting of rigid diatomic molecules was initially under standard conditions. Then gas was compressed adiabatically to one fifth of its initial volume. What will be the mean kinetic energy

A gas consisting of rigid diatomic molecules was initially under standard conditions. Then gas was compressed adiabatically to one fifth of its initial volume. What will be the mean kinetic energy of a rotating molecule in the final state?
 

Option: 1

1.44 \mathrm{~J}


 


Option: 2

4.55 \mathrm{~J}
 


Option: 3

787.98 \times 10^{-23}
 


Option: 4

{757.3 \times 10^{-23} \mathrm{~J}}


Answers (1)

best_answer

\gamma=1.4

\mathrm{T V^{\gamma-1}=\text { constant } }

\mathrm{ \mathrm{T}_1 \mathrm{~V}_1^{\gamma-1}=\mathrm{T}_2 \mathrm{~V}_2^{\gamma-1} }

\mathrm{ (300) \mathrm{V}_1{ }^{7 / 5-1}=\mathrm{T}_2\left(\frac{V_1}{5}\right)^{\frac{7}{5}-1} }

\mathrm{ T_2=\frac{300 \times V_1^{2 / 5}}{V_1^{2 / 5} \times\left(\frac{1}{5}\right)^{2 / 5}}=\frac{300}{5^{-2 / 5}}=300 \times 5^{2 / 5}=300 \times(1.903)=571 }

Mean kinetic energy of rotating molecules \mathrm{ =\mathrm{KT}=1.38 \times 10^{-23} \times 571\: \mathrm{KT}=787.98 \times 10^{-23} }

 

Posted by

avinash.dongre

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