Answer to Question #100509 in Molecular Physics | Thermodynamics for Harsha

Question

A gas sample at 0C is heated until the average velocity of its molecules doubles. What is its new temperature?

Answer 1

Average velocity of gas molecules = (8RT/$\pi$M)^1/2

where T being the temperature in kelvin , M is the molecular mass

we can say that velocity is directly proportional to the square root of T

then, V₁/V₂ =(T₁/T₂)^1/2

as velocity gets doubled so V₁/V₂ = 1/2

so, 0.5= (273/T₂)^1/2

T₂ = 273/0.25

=1092 K

In ⁰C =1092-273 = 819 ⁰C