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  • Gas at pressure  is contained in a vessel. If the masses of all the molecules are do

Gas at pressure \mathrm{P_{0}}  is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure \mathrm{P} will be equal to

Option: 1

2 \mathrm{P}_{0}


Option: 2

\quad \mathrm{P}_{\mathrm{o}} / 4


Option: 3

\mathrm{P}_{\mathrm{o}}


Option: 4

\mathrm{P}_{\mathrm{o}} / 2


Answers (1)

best_answer

\mathrm{P_{0}=\frac{1}{3}\left(\frac{\mathrm{mn}}{\mathrm{v}}\right) \mathrm{v}_{\mathrm{ms}}^{2}}

\mathrm{P=\frac{1}{3}\left(\frac{m^{\prime} n}{v}\right) v_{r m s}^{\prime 2}}

\mathrm{where \, m^{\prime}=2 m, v_{r m s}^{\prime}=\frac{v_{\mathrm{rms}}}{2}}
putting the value
\mathrm{\therefore \quad \frac{P}{P_{0}} =\frac{m^{\prime} v_{r m s}^{\prime 2}}{m v_{r m s}^{2}}=\frac{2 m}{m} \frac{v^{2}{ }_{r m s}}{4 \times v^{2}{ }_{r m s}}=\frac{1}{2} }
\mathrm{P=P_{0} / 2 }

Posted by

Deependra Verma

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