A closed vessel of fixed volume contains a mass m of an ideal gas, the root mean square speed being v. Additional mass m of the same gas is pumped into the vessel and the pressure rises to $$2$$ P, the temperature remaining the same as before. The root mean square speed of the molecule now is

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Infinity Learn · Accepted Answer

$$PV=(m/M)RT(M=$$ molecular mass $$)$$       ....(1)P$$′$$V=(2m/M)RT$$                                             ....$$(2)           From eqs. (1) and (2),P′$$P=21Now$$,   $$Vrms=3P$$ρ$$=3P(m/V)$$            ....(3)and$$     vrms′$$=3P$$′$$(2m/V)                           ...(4)From$$ eqs. $$(3) and (4),vrms′$$vrms=12P$$′$$P=12(2)=1vrms$$′$$=vrms$$

A closed vessel of fixed volume contains a mass m of an ideal gas, the root mean square speed being v. Additional mass m of the same gas is pumped into the vessel and the pressure rises to 2 P, the temperature remaining the same as before. The root mean square speed of the molecule now is

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