Exercise \(\PageIndex{1}\)
Consider a system of two objects in
contact, one initially hotter than the other, so they may directly
exchange thermal energy, in isolation from the rest of the world.
According to the laws of thermodynamics, what must happen to the
system’s total energy and entropy? (Do they change, increase,
decrease, stay constant...?)
Exercise \(\PageIndex{2}\)
Consider the same two objects in
Problem 1 and suppose the heat capacity of the colder object is
much greater than the heat capacity of the hotter one. When the
system reaches thermal equilibrium, will its final temperature will
be closer to the initial temperature of the hot object, the colder
object, or exactly halfway between the two initial temperatures?
Why?
Exercise \(\PageIndex{3}\)
Which of the following is
not a valid formulation of the second law of
thermodynamics?
- For any system in thermal equilibrium, there exists a state
variable, called entropy, with the property that it can never
decrease for a closed system.
- No process is possible whose sole result is the transfer of
heat from a cooler to a hotter body.
- It is impossible for an engine that operates in a cycle, taking
in heat from a hot reservoir at temperature \(T_h\) and exhausting
heat to a cold reservoir at temperature \(T_c\), to do work with an
efficiency greater than \(1 − T_c/T_h\).
- The entropy of any system goes to zero as \(T\) (the absolute,
or Kelvin) temperature goes to zero.
Exercise \(\PageIndex{4}\)
Which of the following statements is
true?
- Once the entropy of a system increases, it is impossible to
bring it back down.
- Once some amount of mechanical energy is converted to thermal
energy, it is impossible to turn any of it back into mechanical
energy.
- It is always possible to reduce the entropy of a system, for
instance, by cooling it.
- All of the above statements are true.
- None of the above statements are true.
Other Questions
- Can you tell the temperature of a gas
by measuring the translational kinetic energy of a single
molecule?
- Does a shuffled deck of cards have
more or less entropy (in the thermodynamic sense) than an
identical, ordered set of cards? Assume they are at the same
temperature.
- A diatomic gas molecule, such as
\(O_2\), can store kinetic energy in the form of vibrations and
rotations, in addition to just translation of the center of mass.
By contrast, a monoatomic gas molecule such as \(C\) has virtually
no kinetic energy (at normal temperatures) other than translational
kinetic energy. Which kind of gas do you expect to have a larger
molar heat capacity (heat capacity per molecule)?