The variation of the molar Gibbs free energy of a substance with temperature and pressure is given by \[ \bar{G} = -T \ln \left( \frac{T^{5/2}}{P} \right) \] Determine \(\bar{S}, \bar{H}, \bar{V}, \bar{U}\) and \(\bar{F}\).
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- 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 = JA 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 = _____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,
- Needs Complete solution with 100 % accuracy.The energy generation rate for the CNO thermonuclear cycle is given by the following propor- tionality relation 1/37 exp[-152 (109)]. T ECNO X T-2/3 exp-152 If the energy generation rate is approximated by a power law as e x Tº at a given temperature T, then a is given by a = din. Hence show that ECNO x T¹8 at T = 2.0 × 107 K. In TFor a dilute gas of N monatomic particles with mass m and total energy E, use the Sackur- Tetrode equation for the entropy S V = log + NkB to derive expressions for the pressure and internal energy in terms of the temperature T and volume V. [You may use that X₁ = 3πh² N/(mE).] th
- The exact differential for the Gibbs energy is given by dG = -SdT + VdP. The form of this differential implies which of the following relationships? O (7),- (), ƏG Әт ƏG др P T (37), - - (-), P T as ( x) - (*), = др T (327), = -(0)₁ == P TUsing the same procedure to determine the fundamental equation of chemical thermodynamics (dG = –SdT + VdP) from the Gibbs free energy of a system (G = H – TS), can you please explain how to find the analogous fundamental equation for (A=U-TS)? Also, can you please handwrite the formula down instead of typing? I get confused with typed formulas sometime.