Question

The velocity of sound in a gas at temperature 27 c is v thenin same gas its velocity willl be 2v at temperature?

Answer 1

according to me this is the answer
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comment if correct
and
sorry for my handwriting

Answer 2

The temperature in which the velocity become 2v will be

Given

The velocity of sound in a gas at temperature 27 c is v

To Find

We need to find the temperature in which the velocity become 2v .

Solution

According to the Kinetic theory of Gases,

The rms velocity is directly proportional to the square root of temperature and inversely proportional to the square root of molar mass.

V α√T

At first case,

 $V_{1}$ α√(27+273)                           T = 27+273 = 300K

     α√300

At second case

 $V_{2}$ α √T

Comparing the equations we get,

  $V_{1}$ /   $V_{2}$  =  $\frac{\sqrt{300} }{\sqrt{T} }$

       $\frac{V}{2V}$     =  $\frac{\sqrt{300} }{\sqrt{T} }$

           $\frac{1}{2}$   =  $\frac{\sqrt{300} }{\sqrt{T} }$

         √T  = 2 × √300

            T = 4 × 300 = 1200 K

                                = 927° C

The temperature in which the velocity become 2v will be 927° C.

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