Question

At what temperature is the velocity of sound in nitrogen is equal to half its velocity in oxygen at 25degree Celsius? ( The ratio of molecular weights of nitogen and oxygen is 7:8 )

Answer 1

the relation between velocity of sound and temperature is given as

v = (γRT / M)1/2

now

for hydrogen

vH =  (γRTH / MH)1/2

here TH = 273 K

MH = 1g/mol

so,

vH =  (γR x 273 / 1)1/2

for oxygen

vo =  (γRTO / MO)1/2

here

MO = 32 g/mol

so,

vo =  (γRTO / 32)1/2

now as per given

vH = vo

so,

(γR x 273 / 1)1/2 = (γRTO / 32)1/2

or

273 = TO / 32

thus,

TO = 273 x 32 = 8736 K