At what temperature is the average velocity of O2 molecule equal to the root mean square velocity at 27°C

uav=vrms8RTπm=3RTm8RTπm=3RTm⇒8RTπm=3R×300mT=353.57Kt=80.57∘C

At what temperature is the average velocity of O2 molecule equal to the root mean square velocity at 27°C

uav=vrms8RTπm=3RTm8RTπm=3RTm⇒8RTπm=3R×300mT=353.57Kt=80.57∘C

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At what temperature is the average velocity of O₂ molecule equal to the root mean square velocity at 27°C

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80.57°C

80°C

83°C

86.5°C

answer is A.

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$\begin{array}{l} u_{av} = v_{rms} \\ \sqrt{\frac{8 RT}{πm}} = \sqrt{\frac{3 RT}{m}} \\ \frac{8 RT}{πm} = \frac{3 RT}{m} \Rightarrow \frac{8 RT}{πm} = \frac{3 R \times 300}{m} \\ T = 353 .57 K \\ t = 80 {.57}^{\circ} C \end{array}$

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At what temperature is the average velocity of O₂ molecule equal to the root mean square velocity at 27°C