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- 6. If the speed of every atom in a monatomic ideal gas were doubled, by what factor would the Kelvin temperature of the gas be multiplied? (a) 4 (b) 2 (c) 1 (d) } (e)!21. 14-4 Lattice specific heat of a 1D crystal of inert gas atoms. Consider a one-dimensional crystal of inert gas atoms. Let L be the length of the crystal and N the number of atoms. Let a be the lattice constant. . Evaluate the phonon density of states for this crystal. i. Derive an integral expression for the lattice specific heat of the crystal. iii. Evaluate the lattice specific heat in the high- and low- temperature limits.JC-37) Thermal Behavior of Air Air is mostly composed of diatomic nitrogen, N2 oscillator with an effective spring constant of 2.3 x 103 N/m and and effective oscillating mass of half the atomic mass. For what temperatures should vibration contribute to the heat capacity of air? 2. Assume that we can model the gas as an
- A sample of 2.37 moles of an ideal diatomic gas experiences a temperature increase of 65.2 K at constant volume. Find the increase in internal energy if translational, rotational, and vibrational motions are possible.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/KProblem 2: Helium is a very important element for both industrial and research applications. In its gas form it can be used for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 145 moles of Helium gas at room temperature (T = 20° C). The cylinder has a radius of r = 17.5 cm and a height h = 1.45 m. Part (a) What pressure (in kPa) is the helium gas under? P = ______ Part (b) Helium is usually kept in the highest pressure gas cylinders, which can typically withstand at least 500 atm of pressure. Would the tank in part (a) be able to maintain its structural integrity? Part (c) In principle, these tanks could fail if the temperature of the Helium started rising - if they were stored in a hot environment, for instance. To determine how much of a danger this is, calculate the temperature (in C) the Helium gas…
- For any gas, C C. - (+7), (7), Suppose you have one mole of a gas that obeys the equation of state, p(v- b) = represents the volume taken up by the molecules in the system, and 3.5 bars and T = 425 K for your gas sample. Hint: Use the equation of state to evaluate the partial derivatives. =RT, where b is the molar volume. Find the value of A if C-C₁=AR when P = 6The potential energy of two atoms in a diatomic molecule is approximated by U(r) = a/r12-b/r6, where r is the spacing between atoms and a and b are positive constants. Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it - that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. Express your answer in terms of the variables a and b. For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13\times 10-10m and the dissociation energy is 1.54\times 10-18J per molecule. Find the value of the constant a. Express your answer in joules times meter in the twelth power. Find the value of the constant b. Express your answer in joules times meter in the sixth power.C A F D B E V
- The most probable speed an atom/molecule in an ideal gas in thermodynamic equilibrium at temperatureT will have is vmp=(2kgT/M)/2. What is the most probable speed in a gas of hydrogen molecules (H2) at 77 °C? m,=1.67x10 27 kg, kg=1.38x10 23 J/K.Problem 2: Atmospheric composition A particle near earth's surface traveling faster than about 11km/s has enough kinetic energy to completely escape from the earth, despite earth's gravitational pull. Molecules in the upper atmosphere that are moving faster than this will therefore escape if they do not collide on the way out. a) The temperature of earth’s upper atmosphere is actually quite high, around 1000K. Calculate the probability of a nitrogen molecule at this temperature moving faster than 11km/s, and comment on the result. b) Repeat the calculation for a hydrogen molecule (H2) and for a helium atom, and discuss the implications. c) Escape speed from the moon's surface is only about 2.4km/s. Explain why the moon has no atmosphere.Show that for an ideal gas (@T/ƏV)u = 0, and (@T/ƏP)H= 0.