Answer:
\[P=\frac{1}{3}mn\overline{{{\upsilon }^{2}}}=\frac{1}{3}\frac{mN}{V}\overline{{{\upsilon }^{2}}}\] \[\left[ n=\frac{N}{V} \right]\] (i) As \[P\propto N,\]so the pressure of the gas is doubled when the number of molecules is increased from N to2N. (ii) Average K.E. per molecule, \[\frac{1}{2}m\overline{{{\upsilon }^{2}}}=\frac{3}{2}{{k}_{B}}T\] Total energy of N molecules \[=\frac{1}{2}mN\overline{{{\upsilon }^{2}}}=\frac{3}{2}{{k}_{B}}NT.\] When the number of molecules is increased from N to 2N, total energy of the gas is doubled, though the average K.E. per molecule remains same. (iii) The r. m. s. speed remains same because it depends only upon temperature.
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