Thermodynamics help

Question

A gas is at 200 K. (a) If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? (b) Calculate the increase in pressure during this increase in temperature (assume Pi = 6x104 Pa and a constant volume). (c) At the final temperature, what is the typical (“average”) force transferred to the walls of a 1m3 container by a single molecule colliding with the wall.

Answer 1

a. KE = 1/2 mv²  ∝ T

   ∴ v² ∝ T

 

    v₂²/v₁² = T₂/T₁

 

    T₂ = v₂²/v₁² T1 = (v₂/v₁)². T₁

 

b. Use Gay Lussac's Law. P₂/T₂ = P₁/T₁

 

c. F = P₂ x Area of a wall (assume a cube of side 1 m)