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Question

Gas at a pressure $$P_{o}$$ is contained in a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to:


Solution

$$P= \cfrac {1}{3}\cfrac {mN}{V}V^2_{rms}$$      $$\therefore P \propto mV^2_{rms}$$
So $$\cfrac {P_2}{P_1}=\cfrac {m_2}{m_1}\times \left(\cfrac {V_2}{V_1}\right)^2$$
              $$=\cfrac {m_1/2}{m_1}\left(\cfrac {2V_1}{V_1}\right)^2=2$$
$$\Rightarrow P_2=2P_1=2P_o$$

Chemistry

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