Calculate kB T for T = 500 K in the following units: erg, eV, cm-, wave...

  

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Calculate kB T for T = 500 K in the following units: erg, eV, cm-¹, wave length, degrees Kelvin, and Hertz. The vibrational energy of a diatomic molecule is E, = ħw (v + 1/2), v= 0, 1, 2, .... For H₂, ħ w = 4401 cm-¹. For 1₂, ħw=214.52 cm-¹. Without performing a calculation tell which molecule has higher vibrational entropy. Explain your reasoning. Use ListPlot to make a plot of the probability that an 1₂ molecule has the vibra- tional energy Ev, for v = 1,2,3,4,5,6. Calculate the vibrational entropy of /2 by using the formula giving entropy in terms of probabilities. Plot the vibrational entropy versus temperature in the range T€[298, 700] degrees Kelvin. * Calculate the vibrational entropy of /2 by calculating the vibrational partition function, the vibrational Helmholtz free energy A(T), and then S(T) = -a A(T)/OT (keep N constant). Plot S(T) in the range T€[298, 700] degrees Kelvin. Should you get the same result as in Problem 4? Does the vibrational motion affect the pressure of an ideal gas? Calculate the mean vibrational energy U(T) = Thermodynamics tells us that A(T) = U(T) - T S(T). Verify that this is true. Ev P(Ev) of 1₂ for T = 600K. Calculate kB T for T = 500 K in the following units: erg, eV, cm-¹, wave length, degrees Kelvin, and Hertz. The vibrational energy of a diatomic molecule is E, = ħw (v + 1/2), v= 0, 1, 2, .... For H₂, ħ w = 4401 cm-¹. For 1₂, ħw=214.52 cm-¹. Without performing a calculation tell which molecule has higher vibrational entropy. Explain your reasoning. Use ListPlot to make a plot of the probability that an 1₂ molecule has the vibra- tional energy Ev, for v = 1,2,3,4,5,6. Calculate the vibrational entropy of /2 by using the formula giving entropy in terms of probabilities. Plot the vibrational entropy versus temperature in the range T€[298, 700] degrees Kelvin. * Calculate the vibrational entropy of /2 by calculating the vibrational partition function, the vibrational Helmholtz free energy A(T), and then S(T) = -a A(T)/OT (keep N constant). Plot S(T) in the range T€[298, 700] degrees Kelvin. Should you get the same result as in Problem 4? Does the vibrational motion affect the pressure of an ideal gas? Calculate the mean vibrational energy U(T) = Thermodynamics tells us that A(T) = U(T) - T S(T). Verify that this is true. Ev P(Ev) of 1₂ for T = 600K.

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Problem 1 10 points Calculate kg T for T 500 K in the following units erg eV cm wave length degrees Kelvin and Hertz Answer 1 Erg kgT 138 x 1016 erg 2 eV kgT 862 x 105 eV 3 cm kgT 567 x 105 cm 4 Wave ... View the full answer