The molecules of a given mass of a gas have rms velocity of $$200$$ $$ms-1$$ at $$27$$°C and $$10$$ × $$105$$ $$Nm-2$$ pressure. When the temperature and pressure of the gas are respectively, $$127$$°C and $$0.05$$ × $$105$$ $$Nm-2$$, the rms velocity of its molecules (in$$ $$ms-1) is

Question

The molecules of a given mass of a gas have rms velocity of $$200$$ $$ms-1$$ at $$27$$°C and $$10$$ × $$105$$ $$Nm-2$$ pressure. When the temperature and pressure of the gas are respectively, $$127$$°C and $$0.05$$ × $$105$$ $$Nm-2$$, the rms velocity of its molecules (in$$ $$ms-1) is

Infinity Learn · Accepted Answer

It is given that,     $$vrms1=200$$ $$ms-1$$,$$T1=300$$ K,$$p1=105Nm-2$$           $$T2=400$$ K,$$p2=0.05$$×$$105Nm-2$$,$$vrms2=$$?As, rms velocity of gas molecules,                         vrms ∝ T                            ∵$$vrms=3RTMFor$$ two different cases,⇒             $$vrms1vrms2=T1T2$$⇒$$200vrms2=300400=34$$⇒             vrms $$2=23$$×$$200=4003$$ $$ms-1$$

The molecules of a given mass of a gas have rms velocity of $200 {ms}^{- 1}$ at 27°C and $10 \times 10^{5} {Nm}^{- 2}$ pressure. When the temperature and pressure of the gas are respectively, 127°C and $0.05 \times 10^{5} {Nm}^{- 2}$ , the rms velocity of its molecules (in ${ms}^{- 1}$ ) is

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The molecules of a given mass of a gas have rms velocity of 200 ms-1 at 27°C and 10 × 105 Nm-2 pressure. When the temperature and pressure of the gas are respectively, 127°C and 0.05 × 105 Nm-2, the rms velocity of its molecules (in ms-1) is

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The molecules of a given mass of a gas have rms velocity of $200 {ms}^{- 1}$ at 27°C and $10 \times 10^{5} {Nm}^{- 2}$ pressure. When the temperature and pressure of the gas are respectively, 127°C and $0.05 \times 10^{5} {Nm}^{- 2}$ , the rms velocity of its molecules (in ${ms}^{- 1}$ ) is