Question

Helium gas is filled in two identical bottles A and B. The mass of the gas in the two bottles is 10 gm and 40 gm respectively. If the speed of sound is the same in both bottles, what conclusions will you draw? (Ans: Temperature of B is 4 times the temperature of A.) Solve the example.

Answer 1

"Weight or mass of bottle A is 10 g

Weight or mass of bottle B is 40 g

Let us consider, the sound speed in bottle A and B as V_1 and V_2

If the speed of sound in both the bottles are equal then V_1 = V_2

We know that, V∝ (√T)/(√M)

For V_1 and V_2,

(√T_1)/(√M_1 ) = (√T_2)/(√M_2 )

T_1/M_1 = T_2/M_2

T_1/10 = T_2/40

4T_1 = T_2

That is the temperature of bottle B is four times the temperature of the bottle A."