Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
In a tube filled with oxygen at 300 K , standing waves of frequency 5.0 kHz are generated. The separation between successive nodes is 3.3 cm . Determine the specific heat capacities C_p and C_V of the gas.
Options
- AC_p = 29.0 J K ⁻¹ mol ⁻¹ , C_V = 20.7 J K ⁻¹ mol ⁻¹
- BC_p = 33.2 J K ⁻¹ mol ⁻¹ , C_V = 24.9 J K ⁻¹ mol ⁻¹
- CC_p = 20.7 J K ⁻¹ mol ⁻¹ , C_V = 29.0 J K ⁻¹ mol ⁻¹
- DC_p = 24.9 J K ⁻¹ mol ⁻¹ , C_V = 16.6 J K ⁻¹ mol ⁻¹
Correct answer
A. C_p = 29.0 J K ⁻¹ mol ⁻¹ , C_V = 20.7 J K ⁻¹ mol ⁻¹
Step-by-step solution
The separation between successive nodes in a standing wave is 2 . 2 = 3.3 cm = 6.6 cm = 0.066 m The speed of sound in the gas is: v = f = 5000 0.066 = 330 m/s Using the formula for the speed of sound in an ideal gas, v = R T M : = v^2 M R T = (330)^2 0.032 8.3 300 1.4 We know that C_p - C_V = R and C_p C_V = . C_V = R - 1 = 8.3 1.4 - 1 = 8.3 0.4 = 20.75 20.7 J K ⁻¹ mol ⁻¹ C_p = C_V = 1.4 20.75 = 29.05 29.0 J K ⁻¹ mol ⁻¹