Quickly estimate the change in enthalpy (/mol) to go from CO2 at 223K and 10 bar to 298K and 84 bar.
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- a) Calculate the mean free path in meters of a nitrogen molecule (with a mass m=4.68×10¬26 kg) located in Earth's atmosphere at sea level. Assume a temperature of T=300 K and a number density of particles of 1019 cm-3. b) Assuming that the collision cross-section of the molecule is o = 2x10-10 frequency v in Hertz and the time between collisions t in seconds. m, compute the collisionthe partition function of an ideal gas of diatomic molecules in an external electric field & is [g(V, T, 8)]" Q(N, V, T, 8) N! where (2mmkT 312 (87 IkT -hv/2kT e q(V,T, 8)= V{ h2 (kT' (µ8 sinh kT) h2 (1 – e-hv/kT) Here I is the moment of inertia of the molecule; v is its fundamental vibrational frequency; and u is its dipole moment. Using this partition function along with the thermodynamic relation, dA = -S dT –p dV – M de where M=Nū, where u is the average dipole moment of a molecule in the direction of the external field &, show that kT] coth kT, Sketch this result versus & from & =0 to & =∞ and interpret it.The pressure unit 1 torr is comparable to 0.001 bar. In a sample of N₂ at this pressure and a temperature of 300 K, what is the mean free path between collisions in mm (millimeters)? Assume that the cross-section for N₂ molecules is o = 4.50 × 10-19 m².
- Determine how many times per second each molecule moving with rms speed would move back and forth across a 6.4 mm -long room on the average, assuming it made very few collisions with other molecules.To find vx use the equation v2=v2x+v2y+v2z and the fact that molecules have no preferred direction. vrms= 473 m/sAssume you are using the attached pressure gauge and a thermocouple with a temperature uncertainty of +/- 1C; assuming ideal gas how accurately can you report the molar volume n/V=RT/P?What is the average thermal velocity of a hydrogen molecule H at 27 \deg C? (Assume: Boltzmann constant = 1.38 x 10-23 J/K and the mass of H is m = 3.32 x 10-27 kg)