(1) For a gas that follows equation of state pV = f(T), show that (37) = 1df₁ V av ƏT Р = 1 df p dT
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- Show that for an ideal gas (@T/ƏV)u = 0, and (@T/ƏP)H= 0.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.
- A 0.825 mol sample of NO, (g) initially at 298 K and Molar heat capacity at constant volume (Cy,m) R Туре of gas 1.00 atm is held at constant volume while enough heat is applied to raise the temperature of the gas by 10.3 K. atoms Assuming ideal gas behavior, calculate the amount of heat linear molecules (q) in joules required to affect this temperature change and nonlinear molecules 3R the total change in internal energy, AU. Note that some where R is the ideal gas constant books use AE as the symbol for internal energy instead of AU. q = J AU = J(1) Consider 1 mol of an ideal gas at 300 K and 1 atm pressure. Imagine that the molecules are, for the most part, evenly spaced at the centers of identical cubes. Using Avogadro's constant and taking the diameter of a molecule to be 3 x 10-8 cm, find the length of an edge of such a cube and calculate the ratio of this length to the diameter of a molecule. The edge length is an estimate of the distance between molecules in the gas. (2) Now consider a mole of water having a volume of 18 cm³. Again, imagine the molecules to be evenly spaced at the centers of identical cubes and repeat the calculation in (a).A car tire contains 0.034m^3 of air at a gauge pressure of 2.76x10^5 N/m^2. The composition of air is about 78% nitrogen (N2) and 21% oxygen (O2), both diatomic molecules. How much more internal energy, in joules, does the air in the tire have than the same volume of air has at zero gauge pressure outside the tire? Eint,2 - Eint,1 = _____