CHMY 373 2019 – Problem Set 2
Due: Friday Jan. 25
Reminder: See previous problem set and/or the syllabus for rules regarding problem sets.
Reading: Chapter 19.1‐19.5, Simon & McQuarrie
1. Reversible compression: a reversible process is a thought experiment where every
infinitesimal step of the process represents an equilibrium state. Consider the
reversible compression of 1.0 mole of an ideal gas from 22 L to 2.2 L, at a constant
temperature of 25 °C.
a. Draw a schematic for and describe an experimental setup that would imitate
a reversible compression at constant temperature.
b. Determine the work, heat, and
for this process, in units of kJ.
2. Irreversible compression: one type of irreversible process is a constant pressure
compression or expansion. Consider the constant pressure compression of 1.0 mole
of an ideal gas from 22 L to 2.2 L, at a constant temperature of 25 °C.
a. In the faded instruction manual for this process, it says the process should be
carried out at a constant pressure of either 15 bar or 1.5 bar. Which value
must it be? Hint: one of the two options is impossible to carry out
b. Determine the work, heat, and
for this process, in units of kJ.
3. Chemical reactions can result in work being performed on the environment.
Consider the initial state of a system as follows: 12 g of CaCO3 s lie in a container
fitted with a piston constrained by a fixed external pressure. For the purposes of this
problem, consider the initial volume of the container to be negligible consider all
solids to have a negligible volume . The container is then heated to 1000 °C. During
heating, the sample completely decomposes to CaO s and CO2 g at a temperature of
760 °C.
a. Calculate the work in kJ for the complete process arising from the
mechanical expansion of the system against a fixed external pressure
corresponding to ambient pressure in Bozeman 0.85 bar , assuming that the
gas released is ideal.
b. Do you expect the work to be higher or lower if the CO2 released is “real CO2”
and therefore has a slightly higher volume than an ideal gas at the end of the
process i.e., its compressibility factor, , is greater than 1 at 1000 °C ?
4. The so‐called “
” of a fluid or material is a measure of the
intermolecular forces within it, and is defined by:
,
,
Derive an expression for the internal pressure of:
a. an ideal gas.
b. a van der Waals gas.
c. a Berthelot gas, defined by:
d. a Dietericci gas, defined by:
5. Reversible vs. Free. Consider the expansion of a system containing pure oxygen gas,
which can be fairly accurately described by the van der Waals equation of state see
Table 16.3 for accurate vdW constants . Assume that the molar isochoric heat
of oxygen is 5/2 and is therefore independent of T.
capacity
a. Determine the final temperature, , when 1.0 mole of oxygen undergoes a
reversible adiabatic expansion from
1.0 L to
24 L, if it is initially at
298 K.
b. Determine the final temperature, , when 1.0 mole of oxygen undergoes a
free adiabatic expansion from
1.0 L to
24 L, initially at
298 K.
c. Describe the qualitative relationship between the heat, work, and
of these
two processes i.e., greater than, less than, or equal .