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Two samples \mathrm{A \: and\: B} of a gas are initially at the same temperature and pressure are compressed from volume \mathrm{\mathrm{V}_1\: to \: \mathrm{V} / 2} (\mathrm{A} isothermally and \mathrm{B} adiabatically). The final pressure is
 

Option: 1

\mathrm{A} is greater than that of \mathrm{B}


 


Option: 2

\mathrm{A} is equal that of \mathrm{B}
 


Option: 3

\mathrm{A} is less than that of \mathrm{B}
 


Option: 4

\mathrm{A}  is twice that of \mathrm{B}


Answers (1)

best_answer

\mathrm{For \: \: A, P_{2 A}=P_{1 A}\left(\frac{V_{1 A}}{V_{2 A}}\right)=P_0\left(\frac{V}{V / 2}\right)=2 P_0}

\mathrm{For \: \: \mathrm{B}, \mathrm{P}_{2 \mathrm{~B}}=\mathrm{P}_{1 \mathrm{~B}}\left(\frac{\mathrm{V}_{1 \mathrm{~B}}}{\mathrm{~V}_{2 \mathrm{~B}}}\right)^\gamma=\mathrm{P}_{\mathrm{o}}\left(\frac{\mathrm{V}}{\mathrm{V} / 2}\right)^\gamma=2^y \mathrm{P}_0}

\mathrm{ \therefore \mathrm{P}_{2 \mathrm{~B}}>\mathrm{P}_{2 \mathrm{~A}} . }

 

Posted by

Rakesh

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