Question

To what temperature should hydrogen at 227° C be cooled at constant pressure so that root mean square velocity of its molecule becomes half of its previous value?

Options

• 148° C

• -148° C

• - 123° C

• 123° C

Answer 1

-148° C

Explanation:

`"Using," "v"_rms  prop sqrtT,`

`("v"_"rms")_1/("v"_"rms")_2 = sqrt("T"_1/"T"_2)`.

`"Given that," ("v"_"rms") = ("v"_"rms")_1/2 or ("v"_"rms")_1/("v"_"rms")_2 = 2`

T₁ = 227+273 = 500 K

`therefore 2 = sqrt(500/"T"_2) or`

T₂

`= 500/4 = 125 "K"`

= 125 - 273

= -148° c