Question

calculate the temperature at which rms velocity of gas molecules is double its value at 27oC pressure of the gas remaining the same at what temp is the rms velocity of hydrogen molecules equal to that of an oxygen at 47oC?

Answer 1

Answer:

1) 927⁰C

2) 20⁰K or -253⁰K

Step-by-step explanation:

The internal energy of an ideal gas is proportional to the absolute temperature. The average kinetic energy (rms) of the gas molecules is proportional to the abs temperature.

   P V = n R T    or,    for one molecule :  P V = k T

   avg KE = 1/2 m v² =  3/2 n R T  

   For one molecule the translational kinetic energy with three degress of freedom of movement in 3d space:

          avg KE =  1/2 m v² = 3/2  k T

So rms velocity v is proportional to √T.

       v₂/v₁ = √( T₂ / T₁ )

       2 = √(T₂ / (273+27)

       T₂ = 1200⁰ K or 927⁰C

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2) We assume the conditional of Hydrogen and Oxygen gas molecules are same.  They are both diatomic.

   m₁ v₁² / m₂ v₂² = T₁ / T₂

   m₁ = 2 Hydrogen.       m₂ = 32 Oxygen

   v₁ = v₂  given                  T₂ = 47⁰C = 320⁰K

  So  T₁ = 320⁰ * 2 / 32 = 20⁰ K    or  -253⁰C