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Question: The average kinetic energy of a gas at – 23°C and 75 cm pressure is\(5 \times 10^{- 14}erg\)for\(H_{...

The average kinetic energy of a gas at – 23°C and 75 cm pressure is5×10−14erg5 \times 10^{- 14}ergforH2H_{2}. The mean kinetic energy of the O2O_{2}at 227°C and 150 cm pressure will be

A

(a) 80×10−14erg80 \times 10^{- 14}erg

B

20×10−14erg20 \times 10^{- 14}erg

C

40×10−14erg40 \times 10^{- 14}erg

D

10×10−14erg10 \times 10^{- 14}erg

Answer

10×10−14erg10 \times 10^{- 14}erg

Explanation

Solution

Average kinetic energy

E=32kTE = \frac{3}{2}kT ̃ E1E2=T1T2=(273−23)(273+227)=250500=12\frac{E_{1}}{E_{2}} = \frac{T_{1}}{T_{2}} = \frac{(273 - 23)}{(273 + 227)} = \frac{250}{500} = \frac{1}{2}

̃ E2=2E1=2×5×10−14=10×10−14ergE_{2} = 2E_{1} = 2 \times 5 \times 10^{- 14} = 10 \times 10^{- 14}erg