Consider a system in thermal and diffusive contact with a reservoir. Treat the reservoir as ideal...
Consider a system in thermal and diffusive contact with a reservoir. Treat the reservoir as ideal gas of particles at temperature τ . The system can be in either of the following three states: unoccupied with energy zero, occupied with energy zero (ground state), and occupied with energy ∆ (excited state). (a) Calculate the thermal average occupancy of the ground and excited sates. (b) Find the gas pressure at which the average occupancy of the system is 1/2. (c) Calculate the thermal average energy of the system.
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Consider a system in thermal and diffusive contact with a
reservoir. Treat the reservoir as ideal...
evaluate the integral)? 3) Show that when a system is in thermal and diffusive equilibrium with...
evaluate the integral)? 3) Show that when a system is in thermal and diffusive equilibrium with a reservoir, the average number of particles in the system is N =-ab where Fis the grand partition function, and the partial derivative is taken at fixed temperature and volume. krea where is
7. Consider a system that may be unoccupied with energy zero or occupied by one particle...
7. Consider a system that may be unoccupied with energy zero or occupied by one particle in either of three states, one of energy +e and one of energy -e and one of zero energy. (a) If we assume that there is a maximum of one particle, show that the grand partition function for this system is Z=1+1+Xexp(€/kbT) + Xexp(-e/kBT), where l is related to the chemical potential u by 1 = exp(u/kbT). [4] (b) Show that the thermal average...
2. System of particles obey M-B statistics in thermal equilibrium with its enviroment at temprature T....
2. System of particles obey M-B statistics in thermal equilibrium with its enviroment at temprature T. the percent of occupation of energy levels is given at the table. Energy in ev Energy level propapility percent 0.002 60% 0.011 20% 0.020 8.0% 0.030 1.9% (i) Calculate the temperature of the system. If the vibrationally excited states of nitrogen molecule is given by &, =(n +) @ where n;= 0, 1, 2,..., the differences between anytwo levels is given by ) w=0.5...
Problem 2 Calculate the probability of adsorption of an ideal gas at temperature Ton the surface...
Problem 2 Calculate the probability of adsorption of an ideal gas at temperature Ton the surface with Nindependent (and distinguishable) adsorption sites that are either unoccupied with energy 0, or singly occupied with energy e. The chemical potential of the gas is .
(1.4) Let be a system in contact with three reservoirs: a heat bath, a volume reservoir and a sec...
(1.4) Let be a system in contact with three reservoirs: a heat bath, a volume reservoir and a second work reservoir for other work than volume pressure-work (chemical work for instance). Show that the maximum amount of non-pressure-volume work, W', that can be done by I equals-AG. The equality sign only applies for quasi-static processes. (1.5) According to the second law of thermodynamics, which state function assumes either an extremum in equilibrium for (a) an isolated system (no exchange of...
Consider an 3-dimensional ideal bose gas system whose dispersion relation is given by a) Find the mean occupation numb...
Consider an 3-dimensional ideal bose gas system whose dispersion relation is given by a) Find the mean occupation number of quantum state with a wave vector b) Find the total number of particles at excited states and internal energy at temperature and express it in terms of Bose-Einstein integral and thermal wave length h2k2 E hw 2m We were unable to transcribe this imageWe were unable to transcribe this imageU (T We were unable to transcribe this imagegn(z; h2 1/2...
A system of diatomic ideal gas is in an initial state such that the pressure is...
A system of diatomic ideal gas is in an initial state such that the pressure is 69.0 kPa and the volume occupied by the gas is 6.00 L. The system then experiences a compression at constant temperature that raises the pressure to 165 kPa. (a) Calculate the final volume occupied by the gas. __L (b) Calculate the work done by the gas in this process. (Include the sign of the value in your answer.) __J Please show all work!
One mole of ideal gas is confined in a cylinder by a piston and is in...
One mole of ideal gas is confined in a cylinder by a piston and is in the thermal contact with a heat reservoir with T=To. As a result, gas slowly expands from V1 to V2 while at the same temperature To. The internal energy of the gas does not change. Calculate work done by the gas and the heat flow into the gas.
18. An ideal gas is compressed from a volume of V 5.00 L to a Volume...
18. An ideal gas is compressed from a volume of V 5.00 L to a Volume of V,- 3.00 L while in thermal contact with a heat reservoir of T 295 K. During the compression process the piston moves down a distance of d = 0.130 m under the action of an average external force of F = 25.0 KN. Find (a) the work done on the gas, (b) the change in internal energy of the gas, (c) the thermal...
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of...
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of the energy levels are given by the Bolzmann distribution. (a) What fraction of particles is in the ground state at T = 300 K when the energy spacing is € = 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of...
evaluate the integral)? 3) Show that when a system is in thermal and diffusive equilibrium with a reservoir, the average number of particles in the system is N =-ab where Fis the grand partition function, and the partial derivative is taken at fixed temperature and volume. krea where is
7. Consider a system that may be unoccupied with energy zero or occupied by one particle in either of three states, one of energy +e and one of energy -e and one of zero energy. (a) If we assume that there is a maximum of one particle, show that the grand partition function for this system is Z=1+1+Xexp(€/kbT) + Xexp(-e/kBT), where l is related to the chemical potential u by 1 = exp(u/kbT). [4] (b) Show that the thermal average...
2. System of particles obey M-B statistics in thermal equilibrium with its enviroment at temprature T. the percent of occupation of energy levels is given at the table. Energy in ev Energy level propapility percent 0.002 60% 0.011 20% 0.020 8.0% 0.030 1.9% (i) Calculate the temperature of the system. If the vibrationally excited states of nitrogen molecule is given by &, =(n +) @ where n;= 0, 1, 2,..., the differences between anytwo levels is given by ) w=0.5...
Problem 2 Calculate the probability of adsorption of an ideal gas at temperature Ton the surface with Nindependent (and distinguishable) adsorption sites that are either unoccupied with energy 0, or singly occupied with energy e. The chemical potential of the gas is .
(1.4) Let be a system in contact with three reservoirs: a heat bath, a volume reservoir and a second work reservoir for other work than volume pressure-work (chemical work for instance). Show that the maximum amount of non-pressure-volume work, W', that can be done by I equals-AG. The equality sign only applies for quasi-static processes. (1.5) According to the second law of thermodynamics, which state function assumes either an extremum in equilibrium for (a) an isolated system (no exchange of...
18. An ideal gas is compressed from a volume of V 5.00 L to a Volume of V,- 3.00 L while in thermal contact with a heat reservoir of T 295 K. During the compression process the piston moves down a distance of d = 0.130 m under the action of an average external force of F = 25.0 KN. Find (a) the work done on the gas, (b) the change in internal energy of the gas, (c) the thermal...
3. Consider a canonical system with uniformly spaced energy levels (spacing = €). The populations of the energy levels are given by the Bolzmann distribution. (a) What fraction of particles is in the ground state at T = 300 K when the energy spacing is € = 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of...
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