# Transferred to a system as heat is which is the same

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transferred to a system as heat is which is the same as the expression for the First Law, ) U = q + w q ' w ad & w q ' ) U & w

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Applications/Processes of Thermodynamics The First Law works differently for a process in which the volume stays constant than for a process in which the pressure stays constant Isochoric Process The volume of the system remains constant ( ) V = 0). On a pV diagram, this type of process would be represented by a vertical line. Therefore, there is no area under the curve. Since there is no change in volume, w = 0. So the internal energy of the system depends only on heat transfer. ) U = q V Isobaric Process The system's pressure is fixed ( ) p = 0). It is represented by a horizontal line on a pV diagram. Both w and q will still exist for this process. ) U = q + w
Applications/Processes of Thermodynamics Adiabatic Process There is no transfer of heat to or from the system, ) q = 0, though other characteristics such as the pressure, volume, and temperature of the system may vary. The curve of an adiabatic process on a pV diagram depends on the changes in the system. ) U = w ad Isothermal Process The system's temperature is fixed ( ) T = 0). It is represented by a pV diagram and energy stays constant ( ) U = 0) q = -w Cyclic Process Certain processes have the same initial and final states (e.g., engines). This is represented by a closed path and ) U = 0 q = -w

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Molecular Interpretation of Energy Energy of one atom of a monatomic perfect gas at temperature T : E K ' 1 2 mv 2 x % 1 2 mv 2 y % 1 2 mv 2 z According to Boltzmann, average energy of each term is ½ kT ; mean energy of atoms is three times this, with total energy (3/2) NkT = (3/2 )nRT U m ' U m (0) % 3 2 RT here U m (0) is the internal molar energy at T = 0 (no translation) - so energy can also come from internal structure of atoms If gas has polyatomic molecules, they can rotate about 3 axes as well, for an additional energy contribution of (3/2) RT ( E inc. 2x as rapid as above) U m ' U m (0) % 3 RT Vibration cannot be treated classically - separations between energy levels are very wide - can derive, with the Boltzmann distribution: U m ' U m (0) % N A h < e h < / kT & 1 The right term inc. with temperature, and approaches RT when kT >> h ν . T is increased : internal energy increases: various modes of motion are excited
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