The rms speed of the molecules of a gas is 200 m/s at 27 °C and 1 atm

1.	The rms speed of the molecules of a gas is 200 m/s at 27 °C and 1 atmosphere pressure. The rms speed at 127 °C and double the pressure is(A) \(\sqrt{\frac{800}{3}}\)m/s(B) \(\frac{100\sqrt2}3\)m/s(C) \(\frac{400}{\sqrt3}\)m/s(D) \(\frac{800}{3}\)m/s.
Answer» Correct Option is (C) \(\frac{400}{\sqrt3} \ m/s\) \(V_{rms} = \sqrt \frac{3RT}{M}\) \(V_{rms} \times \sqrt T\) \(\frac{V_2}{V_1} = \sqrt \frac{T_2}{T_1}\) \(V_2 = V_1 \times \sqrt \frac{T_2}{T_1}\) = \(200 \sqrt \frac{400}{300}\) \(V_2 = 400 \sqrt \frac{1}{3} \ m/s\) (C) \(\frac{400}{\sqrt3}\)m/s

The rms speed of the molecules of a gas is 200 m/s at 27 °C and 1 atmosphere pressure. The rms speed at 127 °C and double the pressure is(A) \(\sqrt{\frac{800}{3}}\)m/s(B) \(\frac{100\sqrt2}3\)m/s(C) \(\frac{400}{\sqrt3}\)m/s(D) \(\frac{800}{3}\)m/s.

Answer»

Correct Option is (C) \(\frac{400}{\sqrt3} \ m/s\)

\(V_{rms} = \sqrt \frac{3RT}{M}\)

\(V_{rms} \times \sqrt T\)

\(\frac{V_2}{V_1} = \sqrt \frac{T_2}{T_1}\)

\(V_2 = V_1 \times \sqrt \frac{T_2}{T_1}\)

= \(200 \sqrt \frac{400}{300}\)

\(V_2 = 400 \sqrt \frac{1}{3} \ m/s\)