The molecules of a given mass of a gas have root mean square speeds of $$100$$ $$ms-1$$ at $$270C$$ and $$1.00$$ atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at $$1270C$$ and $$2.0$$ atmospheric pressure?

Question

The molecules of a given mass of a gas have root mean square speeds of $$100$$ $$ms-1$$ at $$270C$$ and $$1.00$$ atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at $$1270C$$ and $$2.0$$ atmospheric pressure?

Infinity Learn · Accepted Answer

We know that for a given mass of a gas vrms $$=$$  $$3RTMwhere$$ R is gas constant, T is temperature in kelvin and M is molar mass of the gas.Clearly for a given gas, vrms ∝ T, as R, M are constants.Hence, (vrms)1(vrms)2$$ $$=$$ $$T1T2$$ $$---------(i)Given$$, $$(vrms)1$$ $$=$$ $$100$$ $$m/sT1$$ $$=$$ $$270C$$ $$=$$ $$27$$ $$+$$ $$273$$ $$=$$ $$300$$ $$KT2$$ $$=$$ $$1270C$$ $$=$$ $$127+273$$ $$=$$ $$400$$ K∴ From Eq. $$(i) $$100(vrms)2$$ $$=$$ $$300400$$ $$=$$ $$32$$⇒ $$(vrms)2$$ $$=$$ $$2$$×$$1003$$ $$=$$ $$2003m/s$$

The molecules of a given mass of a gas have root mean square speeds of 100 ${ms}^{- 1}$ at $27^{0} C$ and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at $127^{0} C$ and 2.0 atmospheric pressure?

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The molecules of a given mass of a gas have root mean square speeds of 100 ms-1 at 270C and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 1270C and 2.0 atmospheric pressure?

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The molecules of a given mass of a gas have root mean square speeds of 100 ${ms}^{- 1}$ at $27^{0} C$ and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at $127^{0} C$ and 2.0 atmospheric pressure?