4. A gas confined to move in two dimensions (i.e. molecules on a surface) has a...
4. A gas confined to move in two dimensions (i.e. molecules on a surface) has a speed distribution of ?(?) = ? ?? ?? − ?? 2 2?? . Use this distribution to find vmp, vmean, and vrms for a 2D gas. (Answer:??? = √ ?? ? = √ ?? ? ; ????? = √ ??? ?? = √ ??? ?? ;???? = √ ??? ? = √ ??? ? )
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4. A gas confined to move in two dimensions (i.e. molecules on a
surface) has a...
1. N identical particles of mass m is confined to move only about a surface of...
1. N identical particles of mass m is confined to move only about a surface of area A, and thus can be considered as a “two-dimensional gas.” In the classical limit what is the single particle partition function of one of the particles in this ideal two-dimensional gas? What is the partition function of the N particle gas? What is the mean thermal energy of this gas, and what is the entropy of this gas?
Consider a two-dimensional (2D) Bose gas at finite but low T confined in a square box...
Consider a two-dimensional (2D) Bose gas at finite but low T
confined in a square box potential with side lengths L and area A =
L^2.
2. Consider a two-dimensional (2D) Bose gas at finite but low T confined in a square box potential with side lengths L and area A = L2. Using the density of states function as you found above, derive an expression for the 2D phase space density and argue why Bose-Einstein condensation does not occur...
Molecules in a sample of a gas move at a variety of speeds. Molecular speed can...
Molecules in a sample of a gas move at a variety of speeds. Molecular speed can be described by the root-mean-square speed of the gas, which is the square root of the average of the squares of the speeds of all the gas molecules. What is the rms speed of a sample of O2 at 12.49 °C, in m/s? A typed answer is prefered. Answer should be in significant figures.
Write an expression for the fraction of O_2 molecules that have speed greater than 500 m/s...
Write an expression for the fraction of O_2 molecules that have speed greater than 500 m/s at 300 K. (You do not need to evaluate the integral.) If H_2 molecules are adsorbed on a surface where they are free to move in 2 dimensions, what are <v>, < epsilon _tr>, and v_mp for H_2 molecules on the surface at 250 K? (Assume 2 dimensional ideal gas behavior. See problem 14.17 in the text.)
Consider a particle which is confined to move along the positive x-axis, and that has a...
Consider a particle which is confined to move along the positive x-axis, and that has a Hamiltonian where is a positive real constant having the dimensions of energy. Find the normalized wave function that corresponds to an energy eigenvalue of . The function should be finite everywhere along the positive x-axis and be square integrable. H = 8
5. An ideal gas is confined to a container whose volume is fixed. If the container...
5. An ideal gas is confined to a container whose volume is fixed. If the container holds n moles of gas, by what factor will the pressure increase if the absolute temperature is increased by a factor of 2? (A) 2/(nR) (B) 2 (C) 2nR (D) 2/n (E) 2/R 6. Two large glass containers of equal volume each hold 1 mole of gas. Container 1 is filled with hydrogen gas (2 g/mol), and Container 2 holds helium (4 g/mol). If...
Assume that you have 40000 molecules of carbon dioxide in a box at a temperature of...
Assume that you have 40000 molecules of carbon dioxide in a box at a temperature of 300 K. Also, imagine if the speed distribution of the molecules is governed by the following function N(v) = Ave(-Mv^2/2RT) instead of a Boltzmann distribution N(v) = Av2e(-Mv^2/2RT) Normalize this function to solve for A. Also, solve for the vrms of the carbon dioxide gas. [Use .044 kg/mol for the molar mass of carbon dioxide] Group of answer choices a) A = .706, Vrms = 348.25...
The rms speed of the molecules in 2.0 g of hydrogen gas is 1700 m/s ....
The rms speed of the molecules in 2.0 g of hydrogen gas is 1700 m/s . Part A What is the total translational kinetic energy of the gas molecules? Express your answer to two significant figures and include the appropriate units. ϵtotal ϵ t o t a l = nothing nothing Request Answer Part B What is the thermal energy of the gas? Express your answer to two significant figures and include the appropriate units. Eth E t h =...
Molecules of gas all move at the same average speed, if the temperature is held constant....
Molecules of gas all move at the same average speed, if the temperature is held constant. True False Molecules in liquids are, on average, farther away from each other than the molecules in solids. True False The buoyant force on a Styrofoam sphere that is 10% submerged in water is smaller than the buoyant force on a metal sphere that is 100% submerged in water, if the volumes of the two sphere are equal. True False When a truck and...
The kinetic theory of gases states that the kinetic energy of a gas is directly proportional...
The kinetic theory of gases states that the kinetic energy of a
gas is directly proportional to the temperature of the gas. A
relationship between the microscopic properties of the gas
molecules and the macroscopic properties of the gas can be derived
using the following assumptions: The gas is composed of pointlike
particles separated by comparatively large distances. The gas
molecules are in continual random motion with collisions being
perfectly elastic. The gas molecules exert no long-range forces on
each...
Consider a two-dimensional (2D) Bose gas at finite but low T
confined in a square box potential with side lengths L and area A =
L^2.
2. Consider a two-dimensional (2D) Bose gas at finite but low T confined in a square box potential with side lengths L and area A = L2. Using the density of states function as you found above, derive an expression for the 2D phase space density and argue why Bose-Einstein condensation does not occur...
Write an expression for the fraction of O_2 molecules that have speed greater than 500 m/s at 300 K. (You do not need to evaluate the integral.) If H_2 molecules are adsorbed on a surface where they are free to move in 2 dimensions, what are <v>, < epsilon _tr>, and v_mp for H_2 molecules on the surface at 250 K? (Assume 2 dimensional ideal gas behavior. See problem 14.17 in the text.)
5. An ideal gas is confined to a container whose volume is fixed. If the container holds n moles of gas, by what factor will the pressure increase if the absolute temperature is increased by a factor of 2? (A) 2/(nR) (B) 2 (C) 2nR (D) 2/n (E) 2/R 6. Two large glass containers of equal volume each hold 1 mole of gas. Container 1 is filled with hydrogen gas (2 g/mol), and Container 2 holds helium (4 g/mol). If...
Molecules of gas all move at the same average speed, if the temperature is held constant. True False Molecules in liquids are, on average, farther away from each other than the molecules in solids. True False The buoyant force on a Styrofoam sphere that is 10% submerged in water is smaller than the buoyant force on a metal sphere that is 100% submerged in water, if the volumes of the two sphere are equal. True False When a truck and...
The kinetic theory of gases states that the kinetic energy of a
gas is directly proportional to the temperature of the gas. A
relationship between the microscopic properties of the gas
molecules and the macroscopic properties of the gas can be derived
using the following assumptions: The gas is composed of pointlike
particles separated by comparatively large distances. The gas
molecules are in continual random motion with collisions being
perfectly elastic. The gas molecules exert no long-range forces on
each...
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