Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
A Kundt tube is filled with an ideal gas having a density of 1.7 10⁻³ g cm ⁻³ at a pressure of 1.5 10^5 Pa . When the gas is resonated at a frequency of 3.0 kHz , nodes form at a separation of 6.0 cm . Determine the molar heat capacities C_p and C_V of the gas.
Options
- A26 J K ⁻¹ mol ⁻¹ and 17.7 J K ⁻¹ mol ⁻¹
- B29.1 J K ⁻¹ mol ⁻¹ and 20.8 J K ⁻¹ mol ⁻¹
- C17.7 J K ⁻¹ mol ⁻¹ and 26 J K ⁻¹ mol ⁻¹
- D20.8 J K ⁻¹ mol ⁻¹ and 12.5 J K ⁻¹ mol ⁻¹
Correct answer
A. 26 J K ⁻¹ mol ⁻¹ and 17.7 J K ⁻¹ mol ⁻¹
Step-by-step solution
The distance between two consecutive nodes in a Kundt tube is 2 . 2 = 6.0 cm = 12.0 cm = 0.12 m The speed of sound in the gas is given by: v = f = 3000 Hz 0.12 m = 360 m s ⁻¹ The density of the gas is = 1.7 10⁻³ g cm ⁻³ = 1.7 kg m ⁻³ . The speed of sound is also given by v = P . Squaring both sides and solving for : = v^2 P = (360)^2 1.7 1.5 10^5 = 129600 1.7 150000 = 1.4688 Using the relation C_p - C_V = R and C_p C_V = : C_V = R - 1 = 8.314 1.4688 - 1 = 8.314 0.4688 17.7 J K ⁻¹ mol ⁻¹ C_p = C_V + R = 17.7 + 8.314