Question

Helium gas is filled in two identical bottles A and B. The mass of the gas in two bottles is 10g and 40g respectively. If the speed of sound is the same in both the bottles, what conclusion will you draw?

Answer 1

Given that,

Mass of gas in bottle = m = 10 g

Mass of gas in bottle = M= 40 g

speed of sound in bottle A =speed of sound in bottle B = V

 

Temperature of bottle A = t

Temperature of bottle B = T

Density of bottle A = density of bottle B = D

As we know that,

(Speed of sound in bottle A)/(Speed of sound in bottle B)= [(√M/D)/ (√m/D)] × (√t/√T)

1= (√M/√m)× (√t/√T)

(√T/√t) = (√M/√m)

(√T/√t) = (√40/√10)

(√T/√t) = √4

Taking square on both sides,

T/t = 4

T = 4t

Thus Temperature of bottle B is 4 time greater than Temperature of bottle A.