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Work done by a gas against a changing external pressure
To calculate the work done by a gas against a changing external pressure, it needs to be specified as to how the external pressure is changed.
A process that can be reversed by an infinitely small change in a variable (an infinitesimal change).
A process that cannot be reversed by an infinitesimal change in a variable.
Since it is reversible, use integral calculus:
Calculating the work of a reversible, isothermal expansion of a gas
Why does a reversible process do the most work?
If, during a reverisible expansion of a gas, the external pressure were to be increased any amount at any stage, the piston would move in instead of out. There's no more energy to "resist"…
7.3 Expansion Work Summary
The work done by any system on its surroundings during expansion against a constant pressure is
the energy transferred from one object to another because of a difference in their temperature
a hot coffee mug
energy transfer (Joules)
a process that releases heat to its surroundings
7.4 Heat Summary
Heat is the transfer of energy as a result of a temperature difference. When energy is transferred as heat and no other processes occur, ∆U = q. When energy enters a system as hea…
A thermally isolating wall. In a closed adiabatic system, ∆U = w.
A wall that does permit the transfer of energy as heat.
In the figure above, at which point is the ball's speed about equal to the speed at which it was tossed?
Specific Heat Capacity
Molar Heat Capacity
A measure of how much the temperature of an object is raised when it absorbs heat. C=ΔΗ/ΔΤ
A device in which heat transfer is monitored by recording the change in temperature that it produces, then using q = C₋cal∆T, where C₋cal is the heat capacity of the calorimeter.
Calibrating the Calorimeter
The heat capacity of a calorimeter is determined by supplying a known quantity of hear and noting the resulting rise in temperature.
7.5 The Measurement of Heat Summary
The heat capacity of an object is the ratio of the heat supplied to the temperature rise produced. Heat transfers are measured by using a calibrated calorimeter.
∆U = q + w
The change in internal energy of a closed system is the net result of both heat transfer and work transfer
The First Law of Thermodynamics
The internal energy of an isolated system is constant.
property of the system that changes independently of its pathway
The importance of state functions in thermodynamics
Because a state function depends only on the current state of a system, then if the system is changed from one state to another, the change in a state function is independent of how that change was brought about.
Work is not a state function
EWISOTT; it depends on how the change in a system is brought about. ex. in a reversible process vs. an irreversible process, or expansion vs. free expansion.
Heat is not a state function
EWISOTT; it depends on how the change in a system is brought about. ex. transferring energy to a system by heating it vs. using vibrational energy to excite molecules and raise the temperature.
7.6 The First Law Summary
The first law of thermodynamics states that the internal energy of an isolated system is constant. A state function depends only on the current state of a system. The change in a state function bet…
Energy stored in a system as kinetic energy and potential energy.
Mode of Motion
A way a molecule in a gas can move; each mode can act as a store of energy.
The energy of an atom or molecule due to its motion through space; kinetic energy.
The energy of a molecule (no atoms) due to its rotational motion; kinetic energy.
The energy of a molecule (no atoms) due to the oscillation of its atoms relative to one another; kinetic and potential energy.
The average value of teach quadratic contribution to the energy of a molecule in a sample at a temperature T is equal to ¹/₂ kT.
Translational Mode of Motion
A molecule can move through space along 3 dimensions, so it has three quadratic contributions to the energy (³/₂ kT).
Rotational Mode of Motion
A linear molecule can rotate along 2 dimensions; a nonlinear molecule can rotate along 3. The quadratic contributions to the energy are kT, ³/₂ kT respectively.
Molar Internal Energy
Multiply the total quadratic contributions by Avogadro's constant to get it in terms of #RT.
7.7 A Molecular Interlude: The Origin of Internal Energy Summary
Internal energy is stored as molecular kinetic and potential energy. The equipartition theorem can be used to estimate the translational and rotational contributions to the internal energy of an ideal gas. The vibrational contributio…
The relation between Enthalpy and Heat
Enthalpy at a constant pressure is given by
∆H = q
The change in enthalpy of a system that can do work only by expansion at constant pressure
Units for a change in enthalpy
Since the change in enthalpy is equal to the change in heat energy, it is in terms of Joules.
Endothermic vs. Exothermic
For an endothermic process,
7.8 Heat Transfers at Constant Pressure Summary
The change in enthalpy of a system is equal to the heat supplied to the system at constant pressure. For an endothermic process, ∆H > 0; for an exothermic process, ∆H < 0.
Heat Capacity at Constant Volume
Heat Capacity at Constant Pressure
Molar Heat Capacities of C₋V and C₋P
C₋V = ∆U/∆T
The relation between C₋V and C₋P
C₋P = C₋V + nR
The relation between C₋V,m and C₋P,m
Heat Capacity at constant pressure vs. constant volume
The heat capacity at constant pressure is greater than that at constant volume because at constant pressure, not all the heat supplied is used to raise the temperature; some returns to the surroundings as expan…
7.9 Heat Capacities at Constant Volume and Constant Pressure Summary
The molar heat capacity of an ideal gas at constant pressure is greater than that at constant colume; the two quantities are related by
A graph showing the variation in the temperature of a sample as it is heated at a constant rate at constant pressure, and therefor at a constant rate of increase in enthalpy.
Reading a Heating Curve
A plot of Temperature vs. Heat supplied.
7.12 Heating Curves Summary
The temperature of a sample is constant at its melting and boiling points, even though heat is being supplied. The slope of a heating curve is steeper for a phase with a low heat capa…
Enthalpy changes accompany physical changes, ex. vaporization.
a process in which a substance reacts with oxygen to give heat and light
an equation that includes the quantity of heat released or absorbed during the reaction as written.
The enthalpy corresponding to a certain chemical equation.
Enthalpy of a Reverse reaction
The negative of the enthalpy of the reaction.
7.13 Reaction Enthalpies Summary
A thermochemical equation is a statement of a chemical equation and the corresponding reaction enthalpy, the enthalpy change for the stoichiometric amounts of substances in the chemical equation.
Heat Transfer at constant Volume, Pressure
The heat transfer at constant volume is equal to ∆U.
The relation between ∆H and ∆U
For reactions in no gas is generated or consumed, the difference between ∆H and ∆U is negligible; essentially, ∆H = ∆U.
∆H = ∆U + ∆nRT
Equation for the relation between ∆H and ∆U
7.14 The Relation Between ∆H and ∆U Summary
The reaction enthalpy is less negative (more positive) than the reaction internal energy for reactions that generate gases; for reactions with no change in the amount of gas, the two quantities are almost the same.
Reaction Enthalpy's dependence on State
In calculating the reaction enthalpy, the states of all the substances must be stated, as the heat released or absorbed by a reaction depends on the physical states of the reactants and products.