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Four moles of a substance are distributed over two energy states. The energy of the lower state is zero; the energy of the higher state is 1.5 kJ/mole. At 300 K, what is the value of the Helmholtz free energy (defined as A = U - TS)?
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- The density of gray and white tin are 5.77×103 kg/m3 and 7.37×103 kg/m3. The latent heat for the transition between gray and white tin is 2.20×103 J/mol. The atomic weight of tin is 118.7. Calculate the slope of the tangent of the coexistence curve of gray and white tin at T=376 K. Select one: a.dP/dT=−14.2 atm/K b.dP/dT=−12.9 atm/K c.dP/dT=−14.6 Pa/K d.dP/dT=−12.3 Pa/KThe density of gray and white tin are 5.77 × 10³ kg/m³ and 7.37 × 10³ kg/m³. The latent heat for the transition between gray and white tin is 2.20 x 10³ J/mol. The atomic weight of tin is 118.7. Calculate the slope of the tangent of the coexistence curve of gray and white tin at T = 366 K. Select one: dP dT a. b. d. dT dP dP = -15.8 Pa/K = -14.7 atm/K = -13.3 atm/K = -16.6 Pa/KQUESTION 17 Consider a simple harmonic oscillator with W = 3 x 10+" Hz. At a temperature of 321 K, what is the average internal energy of a single harmonic oscillator in Joules? QUESTION 18 Consider a simple harmonic oscillator with W = 3 x 10+" Hz. At a temperature of 374 K, what is the Helmholtz energy of a single harmonic oscillator in Joules?
- The average thermal energy for a mono-atomic gas is: (kB is Boltzmann constant and T, absolute temperature) kBT kBT kBT1. The expression for free energy as a function of temperature of a system with two states, one at energy 0 and other at 2e is A) F=-k T log(1-2B) F=-k Tlog(1+2) C) F=-k Tlog(1-²0¹²) D)F=-k Tlog(1+²) E) F = k₂Tlog(1+₂³) 2. For a gas of 'N photons having definite frequency w, the specific heat at constant volume is: A) Directly proportional to T C) Directly proportional to T B) Directly proportional to 7¹2 D) Stays constant E) Inversely proportional to TIn a certain physical system, there are two energy states available to a particle: the ground state with energy E₁ = 0 eV, and the excited state with energy E₂ = 1.5 eV. The system is in thermal equilibrium at a temperature T = 300 K. Calculate the Gibbs factor (also known as the Boltzmann factor) for the excited state . Give your answer to two decimal places.
- The binding energy of an electron in a hydrogen atom is 13.6 electron volts. At what temperature will the hydrogen atom’s adiabatic index start to rise, due to the electron and proton being two particles?A container holds N molecules of nitrogen gas at T = 280 K. Find the number of molecules with kinetic energies between 0.0300 eV and 0.0312 eV.(a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)
- One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.In 1995 a research group led by Eric Cornell and Carl Wiemann at the University of Colorado successfully cooled Rubidium atoms to the 20-200 nk temperature range. Assuming (incorrectly) that the Rubidium atoms behave like particles of a classical ideal gas, calculate the RMS speed of a Rubidium atom at a temperature of 36.0 nk. In the experiments one particular isotope of Rubidium was used, Rubidium-87. The molar mass of this isotope is 86.91 g/mol. Submit Answer Tries 0/12In 1995 a research group led by Eric Cornell and Carl Wiemann at the University of Colorado successfully cooled Rubidium atoms to the 20-200 nK temperature range. Assuming (incorrectly) that the Rubidium atoms behave like particles of a classical ideal gas, calculate the RMS speed of a Rubidium atom at a temperature of 53.0 nK. In the experiments one particular isotope of Rubidium was used, Rubidium-87. The molar mass of this isotope is 86.91 g/mol.