Heat Capacity Ratio of Gases

Experiment 1 The kindle Capacity Ratio of Gases Purpose The purpose of this taste is to calculate the heat mental ability ratio of petroles, helium, atomic number 7 and ampere-second Dioxide, and comp ar with their theoretical values. Introduction Thermodynamics is the bailiwick of heat as it relates to vital force and work. There are various properties which all relate to each some other when determining the characteristic of a certain substance.One of ofttimes(prenominal) properties is heat mental ability, which is the amount of heat cipher essential to raise the temperature of a substance by cardinal degree Kelvin. Mathematically, it is ? = q? T , where q is the amount of heat absorbed by a substance and ? T is the alter in temperature measured. When substances absorb heat, their molecules translate, rotate and vibrate callable to the rise in temperature . As a solvent of the motion of perishment of molecules in these modes, there is a component of energy toward s determining the heat cogency of that substance.The heat capacity is, however, defined through constant multitude (Cv) or constant pressure (Cp) with a relationship, Cp = Cv + nR and CpCv , the heat capacity ratio for perfection gases which is further determined by obtaining the pressure divergency with atomospheric pressure in adiabatic conditions. That is lnp1-lnp2lnp1-lnp3. The energy percentage through the modes of guidement of molecules is the total of their, expositional, rotational and tingleal energies. For ideal gases, this can be reason theoretically as a result of their classes, Monatomic, Diatomic and unidimensional polyatomic.Monatomic gases such as Helium, move in translation with the energy 32RT. Diatomic gases such as Nitrogen, move in all 3 modes with the energy 72RT. And the running(a) polyatomic gases such as CO2 move with the energy 132RT. The constant volume heat capacity for these ideal gases can be determined as a result of its relationship with t hese energies as the energy U = nRT and Cv is the derivative with respect to volume. i. e Cv = ? U? Tv . This leads to the following Cv for the 3 classes of gases 12. 5 Jmol*K for monatomic, 29.1 Jmol*K for diatomic, and 54. 0 Jmol*K for linear polyatomic. Data Room Temperature = 16. 2 oC 0. oC p2 = Room Pressure Room Pressure = 760. 84 mmHg 0. 22 mmHg Helium mental testing P1 (mmHg)(0. 3) P3 (mmHg)(0. 3) 1 300. 4 75. 6 2 275. 7 69. 0 3 281. 9 74. 8 Carbon Dioxide effort P1 (mmHg)(0. 3) P3 (mmHg)(0. 3) 1 290. 3 34. 1 2 277. 8 25. 3 3 283. 1 40. 1 The values for Helium and Carbon dioxide were gotten from the other group who performed the experiment. Nitrogen Trial P1 (mmHg)(0. 3) P3 (mmHg)(0. 3) 1 278. 7 63. 7 2 286. 6 89. 7 3 270. 5 58. 9 4 294. 2 85. 0 5 285. 5 89. 7 6 291. 4 70. 0 7 268. 1 54. 1 8 289. 0 64. 8 9 281. 5 65. 8 10 265. 3 59. 7Values in bold are the 3 best trial obtained. Answers to Questions 1) C, mathematical defined as C = q? T , is the heat capacity, the amoun t of energy required to raise the temperature of a substance by one degree Kelvin. Cv, is the heat capacity per whole volume while, Cp , is the heat capacity per unit pressure. two are related mathematically by the comparison Cp = Cv + nR. The expected heat capacity for the triplet classes of gases are as follows Monatomic = 3R2=12. 5 Jmol. K Diatomic = 7R2=29. 1 Jmol. K Linear triatomic = 13R2=54. 0 Jmol. K The equations leading to the heat capacity ratio, ? , is summarized by CpCv= ln(p1p2)ln? p1p3) The vibrational part to Cv can be determined once the vibrational frequencies of the molecule is known. That is Rx2e-x where is x5 . x = (NA hRT)v Where NA = Avogadros number, h = Plancks constant and v = vibration frequency.2) Data obtained in the experiment is presented in the information section above. 3) Sample fracture calculation 2300. 42*0. 32+760. 842*0. 222 =817. 9962127 2817. 99621271061. 242+0. 22760. 842 = 0. 770793 275. 62*0. 32+760. 842*0. 222 =168. 9143383 2817. 99 621271061. 242+168. 9143383836. 442 = 0. 79681 0. 7707931. 39482677 = 0. 55261 0. 796811. 26875807 = 0. 6280336 20. 552610. 327702282+0. 62803361. 268758072 = 3. 12 This was employ to calculate all errors in the heat capacity ratios below. Helium Trial ? = ln(p1p2)ln? (p1p3) Error 1 ln(300. 4+760. 84760. 84)ln? (300. 4+760. 8475. 6+760. 84) = 1. 40 3. 12 2 ln(275. 7+760. 84760. 84)ln? (275. 7+760. 8469. 0+760. 84) = 1. 39 3. 12 3 ln(281. 9+760. 84760. 84)ln? (281. 9+760. 8474. 8+760. 84) = 1. 43 3. 12 Carbon Dioxide Trial ? = ln(p1p2)ln? (p1p3) Error 1 ln(290. 3+760. 84760. 84)ln? (290. 3+760. 8434. 1+760. 84) = 1. 16 3. 08 2 ln(277. 8+760. 84760. 84)ln? (277. 8+760. 8425. 3+760. 84) = 1. 12 3. 07 3 ln(283. +760. 84760. 84)ln? (283. 1+760. 8440. 1+760. 84) = 1. 19 3. 08 Nitrogen Trial ? = ln(p1p2)ln? (p1p3)Error 1 ln(278. 7+760. 84760. 84)ln? (278. 7+760. 8463. 7+760. 84) = 1. 35 3. 11 2 ln(289. 0+760. 84760. 84)ln? (289. 0+760. 8464. 8+760. 84) = 1. 34 3. 11 3 ln(265. 3+760. 84760. 84)ln? (265. 3+760. 8459. 7+760. 84) = 1. 34 3. 11 4) divinatory Cv for CO2 Translation = 3R2 = 3*8. 3142 = 12. 471 Jmol*K Rotational =22 R = 8. 314 Jmol*K vibrational v1 = 4. 02 x 1013 s x = NA hRTv = 6. 02 x 1023*6. 63 x 10-348. 314*2984. 02 x 1013 = 6. 48 consequently contribution = 8. 314(6. 48)2 * e-6. 48 =0. 54 Jmol*K 3 = 7. 05 x 1013 s x = NA hRTv = 6. 02 x 1023*6. 63 x 10-348. 314*298 7. 05 x 1013 = 11. 36 accordingly contribution = 8. 314(11. 36)2 * e-11. 36 = 0. 013 Jmol*K v2 = v4 = 2. 00 x 1013 x = NA hRTv = 6. 02 x 1023*6. 63 x 10-348. 314*298 2. 00 x 1013 = 3. 22 This is less than 5. therefore contribution = 8. 314* 3. 222 *e3. 22e3. 22 -12 = 3. 74Jmol*K Cv for CO2 = 12. 471 +8. 314 +0. 54 +0. 013 + 2(3. 74) = 28. 818 = 29. 0 Jmol*K 5) Cp,m = Cv,m + R so Cv,m = RCp,mCv,m- 1 mediocre experimental ? CO2 = 1. 16+1. 12+1. 193 = 1. 16 Therefore Experimental Cv,m = 8. 3141. 16 1 = 51. 96 = 52. 0 JK While Theoretical Cv,m = 8. 141. 29-1 = 28. 67 = 29. 0 JK Percen tage error = 29 -5229* degree Celsius = 79% 6) Experimental ratio were precise but not accurate to the theoretical values as calculated Gas Average ratio Percentage error (%) Helium 1. 40+1. 39+1. 433 = 1. 41 1. 67-1. 411. 67*100 = 15. 57 Nitrogen 1. 34+1. 34+1. 353 = 1. 34 1. 40-1. 341. 40*100 = 4. 29 Carbon dioxide 1. 16+1. 12+1. 193 =1. 16 1. 29-1. 161. 29*100 = 10. 08 Sources of experimental errors would include leakage through the water connecting the gas cylinder to the adiabatic vessel and the renovate with which the brass cover plate is replaced after the gas expansion.The vibrational contribution to Cv is very much dependent on the temperature. At low temperature, the contribution is zero. As the temperature increases, the lowest vibrational energy is comparable to(predicate) to RT and therefore some contribution to the constant volume heat capacity. While at high temperatures the contribution is at its highest. Conclusion The experiment was successful as the heat capaci ty ratios were achieved to minimal errors from the theoretical values. reference point 1. Thomas Engel, Physical Chemistry, 2nd Edition, Prentice Hall, 2010, pg 21-22, 806 807. 2. science lab manual for Chem 2103, experiment 1. 3. Tip for Experiment 1 on CUlearn.