A closed organ pipe of length 15 cm is filled with oxygen gas ( O₂ ) at 27^ C . An open organ pipe of length 120 cm is filled with hydrogen gas ( H₂ ) at an unknown temperature T^ C . The fundamental frequency of the closed pipe is found to be in unison with the fundamental frequency of the open pipe. Assuming both gases behave as ideal diatomic gases, the value of T is :

Step-by-step solution

Fundamental frequency of closed pipe = v₁ 4 L_c Fundamental frequency of open pipe = v₂ 2 L_o Equating the two frequencies: v₁ 4 15 = v₂ 2 120 v₁ 60 = v₂ 240 v₂ = 4 v₁ The speed of sound in an ideal gas is v = R T M . For diatomic gases, is the same. v₂ v₁ = T₂ M₂ M₁ T₁ Given M₁ = 32 g/mol for O₂ , T₁ = 27^ C = 300 K , and M₂ = 2 g/mol for H₂ : 4 = T₂ 2 32 300 16 = 16 T₂ 300 T₂ = 300 K Converting back to Celsius: T = 300 - 273 = 27^ C Answer: 27