Derive the following expression for the Joule-Kelvin coefficient: 1 = { [r (7), - ] T CP P HjK
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![Derive the following expression for the Joule-Kelvin coefficient:
MJK
1
= /[ r(), - v]
T
Cp
P](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9df25b32-664d-4e03-ac77-887e1e433afe%2F13658d90-f0a2-4a63-b9d0-59105153def3%2Fja0nmoo_processed.png&w=3840&q=75)
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- Cp and Cy are specific heats at constant pressure and constant volume, respectively. It is observed that P C₁ Cv = a for hydrogen gas C₂ - Cy = b for nitrogen gas. The correct relation between a and b is - Cy р (2017 Main) 1 (a) a = b (b) a = 14b (c) a = 28b - b 14 (d) a =A Maxwell-Boltzmann distribution implies that a given molecule (mass m ) will have a speed between 1 and v + dv with probability equal to f(v)dv where ƒ(v) ∞ v² e-mv²/2k³I and the proportionality sign is used because a normalization constant has f(v)dv.) For this distribution, calculate the been omitted. (You can correct for this by dividing any averages you work out by mean speed (v) and the mean inverse speed (1/v). Show that (v)(1/v) = ¼/ .For an iso-enthalpic process, dH = 0. %3D
- a metal is heated, its atoms vibrate more when about their position in the lattice (a netuons of crossed burs) This Causes them to take up more Space, so the solid metal expands from its original shape. calculate the heat needed to expand a ring made of copper internal diameter of Somm to fit over a Shaft of with an diameter So.05mm. The shaft is measured at a temp 182Show that for an ideal gas (@T/ƏV)u = 0, and (@T/ƏP)H= 0.Calculate the number of microstates that are available in a single atom of carbon in graphite.The standard molar entropy (S°) of carbon is 5.7 J/(mol · K) and the Boltzmann constant (kB) is1.381 × 10 ―23?/?. HELP PLEASE
- 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 = JQ When 3.0 mol O, is heated at a constant pressure of 3.25 atm, its temperature increases from 260 K to 285 K. Given that the molar heat capacity of O, (g) at constant pressure is 29.4 J K' mol' calculate q, AH, and AU. The relationship between C, and Cv In the isochoric case no work is done, so the heat fully converts into the internal energy U and the temperature increases. In the isobaric case, theThe variation of the molar Gibbs free pn- ergy of a substance with temperature and pressure is given by () T5/2 G = -T In Determine S, H, V, U and F.
- Consider a system with 1000 particles that can only have two energies, ɛ, and with ɛ, > E,. The difference between these two values is Aɛ = ɛ, -& . Assume that gi = g2 = 1. Using the %3D %3D equation for the Boltzmann distribution graph the number of particles, ni and m, in states & n2, E and E, as a function of temperature for a Aɛ = 1×10-2' J and for a temperature range from 2 to 300 K. (Note: kg = 1.380x10-23 J K-!. %3D %3D (s,-s,) gLe Aɛ/ n2 or = e n,The Z factor is approximately the same for all gases at the same reduced temperature and reduced pressure.