Heat Capacity II

1. CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Heat Capacity II Sound Velocity Method Instructor: Dr. Aleksey I. Filin

2. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Sound Velocity vS can be expressed as: Heat capacity @ constant pressure Where: Heat capacity @ constant volume R – universal gas constant T – temperature M – molecular weight If we know the speed of sound, we can calculate g Instructor: Dr. Aleksey I. Filin

3. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 What the sound is? Definition of sound: Vibrations transmitted through an elastic solid or a liquid or gas, with frequencies in the approximate range of 20 Hz to 20 kHz Characteristics of sound: f – frequency [number of vibrations per unit of time, Hz, or s-1] – wavelength [m] Speed of sound can be found as By definition So, our goal is to measure the wavelength and the frequency of the sound Instructor: Dr. Aleksey I. Filin

4. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Experimental Setup Scope Generator Y1 Y2 t Microphone Speaker If the Generator output is connected to Y1 input of the Scope and the Microphone output is connected to Y2 input, the Scope shows 2 similar sin waveforms. Instructor: Dr. Aleksey I. Filin

5. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Experimental Setup Scope Generator Y X Microphone Speaker If the Generator output is connected to Y1 input of the Scope and the Microphone output is connected to X input, the Scope shows so called Lissajous pattern . A Lissajous pattern is a graph of one frequency plotted on the y axis combined with a second frequency plotted on the x axis. In our case both f are the same Instructor: Dr. Aleksey I. Filin

6. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Mathematical description of the simplest Lissajous pattern Scope shows y as a function of x We know the time dependence both y and x Where Dj is the phase difference between y(t) and x(t) y(t) x(t) Dj Instructor: Dr. Aleksey I. Filin

7. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Mathematical description of the simplest Lissajous pattern y(x) Assuming X0=Y0 If Dj = 0 x y(x)=x If Dj = p/2 (a quarter of period) y(x) x y2(t)+x2(t)=1 Instructor: Dr. Aleksey I. Filin

8. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Mathematical description of the simplest Lissajous pattern y(x) Assuming X0=Y0 y(x)=-x If Dj = p (a half of period) x If Dj = 3p/2 (three quarters of period) y(x) x y2(t)+x2(t)=1 Instructor: Dr. Aleksey I. Filin

9. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Mathematical description of the simplest Lissajous pattern y(x) Assuming X0=Y0 y(x)=x If Dj = 2p (full period) x Full period corresponds to l Note: if X0 = Y0 the angle will be not 450 and the circles become the ellipses Instructor: Dr. Aleksey I. Filin

10. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 How to measure the wavelength? Scope Frequency is given by generator Generator Y Microphone X Speaker Instructor: Dr. Aleksey I. Filin

11. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 How to measure the wavelength? Scope Frequency is given by generator Generator Y Microphone X Speaker Instructor: Dr. Aleksey I. Filin

12. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 How to measure the wavelength? Scope Frequency is given by generator Generator Y Microphone X Speaker Instructor: Dr. Aleksey I. Filin

13. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 How to measure the wavelength? Scope Frequency is given by generator Generator Y Microphone X Speaker Instructor: Dr. Aleksey I. Filin

14. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 How to measure the wavelength? Scope Frequency is given by generator Generator Y Microphone X Speaker Instructor: Dr. Aleksey I. Filin

15. Heat Capacity II Sound Velocity Method CHEM 4396 (W237) Physical Chemistry Laboratory Fall 2009 Summary We measure the shape of Lissajous pattern as a function of microphone position Distance between two positions corresponding to straight 450 line is equal to the wavelength of the sound in given gas at given sound frequency We calculate the speed of sound in given gas at given frequency using formula Instructor: Dr. Aleksey I. Filin