MCAT Physics and Math Review

Chapter 3: Thermodynamics

Conclusion

This chapter reviewed the zeroth law of thermodynamics, which reflects the observation that objects at the same temperature are in thermal equilibrium and the net heat exchanged between them is zero. We may consider the zeroth law to be ex post facto because it provides the thermodynamic explanation for the function of thermometers and temperature scales, which had been developed many years prior to the law’s formulation. We then took some time to define basic thermodynamic terms for systems and state functions. Examination of the first law of thermodynamics revealed that the energy of a closed system (up to and including the universe) is constant, such that the total internal energy of a system (the sum of all its potential and motional energies) equals the heat gained by the system minus the work done by the system. Finally, we carefully investigated the second law of thermodynamics and the concept of entropy. We understand entropy as a measure not only of “disorder” but of the degree to which energy is spread out through a system, up to and including the universe. We now understand that the constant energy of the universe is progressively and irreversibly spreading out and will continue to spread out until there is an even distribution of energy throughout the universe. Many of these concepts will make a reappearance throughout our discussions of general chemistry, and will certainly be seen on the MCAT. In the next chapter, we’ll investigate fluids, the final mechanical concept for Test Day.

Concept Summary

Zeroth Law of Thermod ynamics

·        The zeroth law of thermodynamics states that objects are in thermal equilibrium when they are at the same temperature.

·        Objects in thermal equilibrium experience no net exchange of heat energy.

·        Temperature is a qualitative measure of how hot or cold an object is; quantitatively, it is related to the average kinetic energy of the particles that make up a substance.

·        Thermal expansion describes how a substance changes in length or volume as a function of the change in temperature.

Systems

·        A thermodynamic system is the portion of the universe that we are interested in observing, whereas the surroundings include everything that is not part of the system.

o   Isolated systems do not exchange matter or energy with the surroundings.

o   Closed systems exchange energy but not matter with their surroundings.

o   Open systems exchange both energy and matter with their surroundings.

·        State functions are pathway independent and are not themselves defined by a process. Pressure, density, temperature, volume, enthalpy, internal energy, Gibbs free energy, and entropy are all state functions.

·        Process functions describe the pathway from one equilibrium state to another. Work and heat are process functions.

First Law of Thermodynamics

·        The first law of thermodynamics is a statement of conservation of energy: the total energy in the universe can never decrease or increase.

·        For a closed system, the total internal energy is equal to the heat flow into the system minus the work done by the system.

·        Heat is the process of energy transfer between two objects at different temperatures that occurs until the two objects come into thermal equilibrium (reach the same temperature).

o   Specific heat is the amount of energy necessary to raise one gram of a substance by one degree Celsius or one unit kelvin.

o   The specific heat of water is 

o   During a phase change, heat energy causes changes in the particles’ potential energy and energy distribution (entropy), but not kinetic energy. Therefore, there is no change in temperature. This is the heat of transformation.

·        There are four special types of thermodynamic systems in which a given variable is held constant:

o   For isothermal processes, the temperature is constant, and the change in internal energy is therefore 0.

o   For adiabatic processes, no heat is exchanged.

o   For isobaric processes, the pressure is held constant.

o   For isovolumetric (isochoricprocesses, the volume is held constant and the work done by or on the system is 0.

Second Law of Thermodynamics and Entropy

·        The second law of thermodynamics states that in a closed system (up to and including the entire universe), energy will spontaneously and irreversibly go from being localized to being spread out (dispersed).

·        Entropy is a measure of how much energy has spread out or how spread out energy has become.

·        On a statistical level, as the number of available microstates increases, the potential energy of a molecule is distributed over that larger number of microstates, increasing entropy.

·        Every natural process is ultimately irreversible; under highly controlled conditions, certain equilibrium processes such as phase changes can be treated as essentially reversible.

Answers to Concept Checks

·        3.1

1.    The zeroth law of thermodynamics states that when two objects are both in thermal equilibrium with a third object, they are in thermal equilibrium with each other. By extension, no heat flows between two objects in thermal equilibrium.

2.    While there may be a distance at which thermal equilibrium is impractical, there is no theoretical maximum distance. As long as two objects are in thermal contact and at the same temperature, they are in thermal equilibrium.

3.    Expansion is a result of an increase in dimension at all points along an object. If an object is initially longer, it will experience a greater expansion. This is also represented in the formula for thermal expansion because there is a direct relationship between length change and the initial length of an object.

4.    False. As we will discuss in Chapter 11 of MCAT Physics and Math Review, accuracy is related to an instrument, rather than the scale. In addition, Kelvin uses the same scale as Celsius, so there are no practical differences in terms of accuracy.

·        3.2

1.     

System Type

Transfers Matter

Transfers Energy

Closed

No

Yes

Isolated

No

No

Open

Yes

Yes

2.    State functions are variables independent from the path taken to achieve a particular equilibrium and are properties of a given system at equilibrium; they may be dependent on one another. Process functions define the path (or how the function got to its state) through variables such as Q (heat) or W (work).

3.    State functions include pressure (P), density (ρ), temperature (T), volume (V), enthalpy (H), internal energy (U), Gibbs free energy (G), and entropy (S).

·        3.3

1.    The change in the internal energy of a system is equal to heat put into a system minus the work done by the system. This is the first law of thermodynamics.

2.    Conduction is heat exchange by direct molecular interactions. Convection is heat exchange by fluid movement. Radiation is heat exchange by electromagnetic waves, and does not depend on matter.

3.   

4.    In a P–V graph, work is the area under the curve (or within a closed loop).

·        3.4

1.    On a macroscopic level, entropy can be thought of as the tendency toward disorder. Statistically, entropy is the measure of the spontaneous dispersal of energy at a specific temperature, increasing the number of available microstates for a given molecule.

2.    The entropy of a system and its surroundings will never decrease; it will always either remain zero or increase.

Equations to Remember

(3.1) Temperature conversions:

(3.2) Thermal expansion equation: ΔL = αLΔT

(3.3) Volume expansion equation: ΔV = βVΔT

(3.4) First law of thermodynamics: ΔU = Q – W

(3.5) Heat gained or lost (with temperature change)q = mcΔT

(3.6) Heat gained or lost (phase change)q = mL

(3.7) Entropy and heat

(3.8) Second law of thermodynamics: ΔSuniverse = ΔSsystem + ΔSsurroundings > 0

Shared Concepts

·        Biochemistry Chapter 12

o   Bioenergetics and Regulation of Metabolism

·        General Chemistry Chapter 6

o   Equilibrium

·        General Chemistry Chapter 7

o   Thermochemistry

·        General Chemistry Chapter 8

o   The Gas Phase

·        General Chemistry Chapter 12

o   Electrochemistry

·        Physics and Math Chapter 2

o   Work and Energy