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10. a) Show that, for a system in equilibrium with constant internal energy, the first and...
10. a) Show that, for a system in equilibrium with constant internal energy, the first and...
10. a) Show that, for a system in equilibrium with constant internal energy, the first and second laws together require that dS P dv = 1 b) Determine as for an ideal gas. What are the dimensions of the answer? c) Does the answer to part b make sense given that equilibrium is also the state with the maximum value for the microscopic entropy, defined as S = kp log w?
Learning Goal Internal Energy of an ideal gas The internal energy of a system is the...
Learning Goal Internal Energy of an ideal gas The internal energy of a system is the energy stored in the system. In an ideal gas, the internal energy includes the kinetic energies (translational and rotational) of all the molecules, and other energies due to the interactions among the molecules. The internal energy is proportional to the Absolute Temperature T and the number of moles n (or the number of molecules N). n monatomic ideal gases, the interactions among the molecules...
True or False (Problems 1 through 10) 1. The change in entropy of a closed system...
True or False (Problems 1 through 10) 1. The change in entropy of a closed system is the same for every process between two specified states 2. The entropy of a fixed amount of an incompressible substance increases in every process for which temperature increases 3. A process that violates the second law of thermodynamics violates the first law of thermodynamics. 4. When a net amount of work is done on a closed system undergoing an internally reversible process, a...
Two systems have the following equations of state: 3. T" 2 U0 15 RN) T(2) R is the gas constant. The mole number of the first system is N2 moles, and for the second system Na-3 moles. The t...
Two systems have the following equations of state: 3. T" 2 U0 15 RN) T(2) R is the gas constant. The mole number of the first system is N2 moles, and for the second system Na-3 moles. The two systems are separated by a diathermal wall. (a) If the total energy of the composite system is 2.5*103 J. What is the internal energy of each system in equilibrium? (b) If the initial temperatures rT-250K and T-350K, what is the internal...
2. Consider free expansion of a gas when the internal energy U remains constant. Derive: a) the e...
2. Consider free expansion of a gas when the internal energy U remains constant. Derive: a) the expression for (дт/avJu in terms of P, T, Cv and (ap/aT)v b) the expression for (as/aV)u in terms of P and T c) using equations obtained in a) and b) calculate (expression for) the change of temperature AT and change of entropy AS for a free gas expansion from Vi to V2.
2. Consider free expansion of a gas when the internal energy...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal g...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Write down the equation that defines entropy in thermodynamics. Define...
The first law of thermodynamics In thermal physics, we are often interested in the internal energy...
The first law of thermodynamics In thermal physics, we are often interested in the internal energy (E) of a system. The wo 41 internal energy of an ideal gas is proportional to the temperature and the number of moles of the gas. The internal energy can change when energy is exchanged with the system's environment (ie., objects that are outside the system of interest). The case above is one in which the internal energy of a gas changes due to...
The condition of a system at equilibrium represents a balance between the tendency toward lowest energy...
The condition of a system at equilibrium represents a
balance between the tendency toward lowest energy (E) and
the tendency toward molecular chaos or maximum entropy (S). The
Gibbs Free Energy, G, is the state function that combines energy
and entropy into an equation that allows us to find the balance
between these two tendencies. For a system undergoing change at
constant temperature, ΔG = ΔH - TΔS. The system stops changing when
it reaches the equilibrium condition, ΔG =...
The internal energy, U, is the total energy of a system. For any isolated system, the...
The internal energy, U, is the total energy of a system. For any isolated system, the internal energy is constant. U is a state function, meaning that any path used in calculating AU ill result in the same answer. For any pure substance or fixed mixture of substances, the internal energy, U, can be determined from any two of the variablesP, V, and T. It is often most convenient to choose V and T as the variables. It is helpful,...
6. The formula dS = dQ/T makes it look like a system can only increase its...
6. The formula dS = dQ/T makes it look like a system can only increase its entropy by absorbing heat. You must however remember that this equation is only true for reversible processes. Entropy can change for a system without absorbing any heat. Consider the following scenario. You are given an insulated container with two compartments. The whole container is at the temperature T which remains constant. One compartment has a volume V1 and has n1 moles of an ideal...
10. a) Show that, for a system in equilibrium with constant internal energy, the first and second laws together require that dS P dv = 1 b) Determine as for an ideal gas. What are the dimensions of the answer? c) Does the answer to part b make sense given that equilibrium is also the state with the maximum value for the microscopic entropy, defined as S = kp log w?
Learning Goal Internal Energy of an ideal gas The internal energy of a system is the energy stored in the system. In an ideal gas, the internal energy includes the kinetic energies (translational and rotational) of all the molecules, and other energies due to the interactions among the molecules. The internal energy is proportional to the Absolute Temperature T and the number of moles n (or the number of molecules N). n monatomic ideal gases, the interactions among the molecules...
True or False (Problems 1 through 10) 1. The change in entropy of a closed system is the same for every process between two specified states 2. The entropy of a fixed amount of an incompressible substance increases in every process for which temperature increases 3. A process that violates the second law of thermodynamics violates the first law of thermodynamics. 4. When a net amount of work is done on a closed system undergoing an internally reversible process, a...
Two systems have the following equations of state: 3. T" 2 U0 15 RN) T(2) R is the gas constant. The mole number of the first system is N2 moles, and for the second system Na-3 moles. The two systems are separated by a diathermal wall. (a) If the total energy of the composite system is 2.5*103 J. What is the internal energy of each system in equilibrium? (b) If the initial temperatures rT-250K and T-350K, what is the internal...
2. Consider free expansion of a gas when the internal energy U remains constant. Derive: a) the expression for (дт/avJu in terms of P, T, Cv and (ap/aT)v b) the expression for (as/aV)u in terms of P and T c) using equations obtained in a) and b) calculate (expression for) the change of temperature AT and change of entropy AS for a free gas expansion from Vi to V2.
2. Consider free expansion of a gas when the internal energy...
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Write down the equation that defines entropy in thermodynamics. Define...
The first law of thermodynamics In thermal physics, we are often interested in the internal energy (E) of a system. The wo 41 internal energy of an ideal gas is proportional to the temperature and the number of moles of the gas. The internal energy can change when energy is exchanged with the system's environment (ie., objects that are outside the system of interest). The case above is one in which the internal energy of a gas changes due to...
The condition of a system at equilibrium represents a
balance between the tendency toward lowest energy (E) and
the tendency toward molecular chaos or maximum entropy (S). The
Gibbs Free Energy, G, is the state function that combines energy
and entropy into an equation that allows us to find the balance
between these two tendencies. For a system undergoing change at
constant temperature, ΔG = ΔH - TΔS. The system stops changing when
it reaches the equilibrium condition, ΔG =...
The internal energy, U, is the total energy of a system. For any isolated system, the internal energy is constant. U is a state function, meaning that any path used in calculating AU ill result in the same answer. For any pure substance or fixed mixture of substances, the internal energy, U, can be determined from any two of the variablesP, V, and T. It is often most convenient to choose V and T as the variables. It is helpful,...
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