Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 38

2.2 1 Given the ideal gas law, pV = nRT , find q for an isothermal reversible
expansion. What is the work required to compress 1 mol of an ideal gas
from 1 to 100 atm at room temperature? Express the work in J, erg, cal,
and L atm units. Note that the latter three are not SI units.
2.3 2 For an ideal gas show that, for an adiabatic expansion, TV r is a constant
and r is given by R/C v .
2.4 2 For an ideal gas show that the difference between C p and C v is the gas
constant, R .
2.5 1 Calculate the rate of change in temperature per height for the rise of a
1-g dry air parcel in the lower atmosphere. The actual rate is 6.5 EC/km.
Suggest reasons for the difference. C p , m = 1.005 kJ/kg/ ◦ C.
2.6 2 Calculate the heat of vaporization of water at 298 K given its value at 393 K
is 2.26 × 10 6 J/kg. The specific heat of water is 4.184 × 10 3 J/K/kg and its
heat capacity at constant pressure is 33.47 J/K/mol. Assume that the heat
capacity is constant within the range of temperature.
2.7 2 Find the heat capacity at constant pressure in J/K/mol for CHCl 3 at 400 K.
Use the data from Table 2.1. Obtain the heat capacity at constant volume
at 400 K.
2.8 2 0.5 m 3 of nitrogen at 400 kPa and 300 K is contained in a vessel insulated
from the atmosphere. A heater within the device is turned on and allowed
to pass a current of 2A for 5 min from a 120-V source. The electrical work
is done on the system to heat the nitrogen gas. Find the final temperature
of the gas in the tank. C p for nitrogen is 1.039 kJ/kg K.
2.9 2 A 5-L tank contains 2 mol of methane gas. The pressure of the gas is
increased from 2 to 4 atm while maintaining a constant volume of the
tank. What is the total internal energy change during the process? The heat
capacity at constant pressure for methane is 34 J/mol K and is constant.
2.10 2 A 5-L plastic Coca Cola bottle contains air at 300 K and 12.5 bar gauge
pressure. How much work would the gas do if you could expand the gas
so that the final pressure is 1 bar isothermally and reversibly?
2.13 1 Supercooled water at − 3 ◦ C is frozen at atmospheric pressure. Calculate
the maximum work for this process. The density of water is 0.999 g/cm 3
and that of ice is 0.917 g/cm 3 at

3 ◦ C.
2.14 1 An ideal gas is subjected to a change in pressure from 2 to 20 atm at a
constant temperature of 323 K. Calculate the change in chemical potential
for the gas.
2.15 2 Areactionthatisofconsiderableimportanceinnatureisthetransformation
of methane utilizing ozone, 3CH 4 ( g ) + 4O 3 ( g ) → 3CO 2 ( g ) + 6H 2 O(l).
The above reaction is the main source for water in the stratosphere and is
augmented by photochemical processes.
(a) Let us carry out the reaction in a laboratory at 298 K. If the standard
heat of formation of ozone is 142 kJ/mol and those of carbon dioxide,
water, and methane are, respectively, − 393, − 285, and − 75 kJ/mol
at 298 K, determine the standard heat of the overall reaction at 298 K.
Compare this enthalpy change with the reaction of methane with
oxygen in the previous problem.
(b) If the standard Gibbs free energy of the formation of ozone, carbon
dioxide, water, and methane are, respectively, 163, − 394, − 237, and
− 50 kJ/mol at 298 K, calculate the standard free energy change of
the overall reaction at 298 K.

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