The energy of an ideal gas with a fixed number of molecules (monatomic or polyatomic) can be written solely as a
function of temperature.
Calculation of the dry adiabatic lapse rate:
Heat capacities of solids are normally measured
Consider a possible relationship between the heat capacity at constant pressure
and at constant
volume
:
where
is Boltzmann’s
constant and
is
the number of atoms/molecules. Choose the statement that best describes the validity of this relationship:
In Joule’s experiment two gas cylinders are initially connected by a valve and in thermal contact with a surrounding
constant temperature heat bath. One cylinder is initially filled with an “ideal gas” and the other is empty. The valve
connecting the cylinders is opened very quickly, and the gas finally reaches a constant pressure, filling both cylinders.
From start to finish, the entropy of the ideal gas has:
Consider 7 symbols of 3 types: there are 2 indistinguishable ’
*’ symbols; there are 3 indistinguishable ’
|’ symbols;
and there are 2 indistinguishable ’
X’ symbols. Consider writing all of these symbols out: e.g. ’
|X||X**’ How many
distinct ways can these 7 symbols be written out in this manner?
If we define pressure as:
we can also say:
The expression
holds for:
A heat engine based on the Diesel cycle:
The coefficient of performance (COP) of a refrigerator can be defined as
where
is the work done
per cycle and
is the heat extracted from the cold reservoir. The COP:
If we know the change in Gibbs free energy for a process starting and finishing in equilibrium states,
we can say
that
As a particular solid material melts into a liquid, its volume increases. It is observed that the melting temperature
for the solid increases as pressure decreases. If the solid melts into a liquid at constant temperature, the entropy
of the sample:
An electric stove is used to heat water from
to
on
top of a mountain.
Consider a closed container of air and liquid water at room temperature and pressure.
At equilibrium, the partial pressure of water within the air:
Suppose that we have water at
and
. If we increase the
pressure on the water to
(keeping the same temperature), the Gibbs free energy will change. To compensate for this change (i.e. make Gibbs free energy
the same as at
)
we:
The time required to cook pasta at higher elevations:
A phase diagram for a specific material exhibits
along a boundary between its solid and liquid phases. We can definitively say:
Although graphite is more thermodynamically stable than diamond at room temperature and pressure, we can make
diamond more stable than graphite by:
Consider the efficiency
of a fuel cell, defined as:
where
,
and
(below)
are for the fuel cell system (not fuel cell and environment). The efficiency: