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2 Work, Heat, and Energy: The First Law of Thermodynamics
Exercise 2.26
Using the values of a, b, and c from Table A.6, calculate the values of C P,m for O 2 gas at 298.15 K,
500.0 K, 1000.0 K, and 2000.0 K. Compare with the values in Table A.8.
A transition between two phases of a single substance takes place at a definite
temperature if the pressure is fixed. For example, if the pressure is fixed at 1.000 atm,
the boiling temperature of water is 100.00 ◦ C or 373.15 K and its freezing temperature
is 0.00 ◦ C or 273.15 K. Table A.7 gives specific enthalpy changes (enthalpy changes
per gram) for reversible fusion (melting) and vaporization (boiling) transitions for a
number of substances at a constant pressure of 1.000 atm.
To obtain the molar enthalpy change from the specific enthalpy change, one multiplies the specific enthalpy change by the molar mass in grams per mole. To calculate
∆H for the fusion of n moles of a substance we write
∆H n∆ fus H m
(2.6-2)
where ∆ fus H m is the molar enthalpy change of fusion. For the vaporization of n moles
of a substance
∆H n∆ vap H m
(2.6-3)
where ∆ vap H m is the molar enthalpy change of vaporization of the substance.
E X A M P L E 2.25
Find ∆H and q if 2.000 mol of liquid water at 0.00 ◦ C is reversibly frozen to ice at 0.00 ◦ C at
a constant pressure of 1.000 atm.
Solution
q ∆H (2.000 mol)
18.02 g mol −1
−333.5 J g −1
−1.202 × 10 4 J
Since the enthalpy is a state function, we can calculate ∆H for a given process by
calculating ∆H for any process having the same initial and final states.
E X A M P L E 2.26
Calculate ∆H for the change of state of 1.000 mol of helium from a volume of 5.000 L and
a temperature of 298.15 K to a volume of 10.000 L and a temperature of 373.15 K. Assume
that C P,m 5R/2 and assume that the gas is ideal.
Solution
The value of ∆H is path-independent. For purposes of calculation, assume that the gas first
expands isothermally and reversibly to a pressure equal to the final pressure (step 1), and is
then heated at constant pressure to its final temperature (step 2). Since the enthalpy depends
2 Work, Heat, and Energy: The First Law of Thermodynamics
Exercise 2.26
Using the values of a, b, and c from Table A.6, calculate the values of C P,m for O 2 gas at 298.15 K,
500.0 K, 1000.0 K, and 2000.0 K. Compare with the values in Table A.8.
A transition between two phases of a single substance takes place at a definite
temperature if the pressure is fixed. For example, if the pressure is fixed at 1.000 atm,
the boiling temperature of water is 100.00 ◦ C or 373.15 K and its freezing temperature
is 0.00 ◦ C or 273.15 K. Table A.7 gives specific enthalpy changes (enthalpy changes
per gram) for reversible fusion (melting) and vaporization (boiling) transitions for a
number of substances at a constant pressure of 1.000 atm.
To obtain the molar enthalpy change from the specific enthalpy change, one multiplies the specific enthalpy change by the molar mass in grams per mole. To calculate
∆H for the fusion of n moles of a substance we write
∆H n∆ fus H m
(2.6-2)
where ∆ fus H m is the molar enthalpy change of fusion. For the vaporization of n moles
of a substance
∆H n∆ vap H m
(2.6-3)
where ∆ vap H m is the molar enthalpy change of vaporization of the substance.
E X A M P L E 2.25
Find ∆H and q if 2.000 mol of liquid water at 0.00 ◦ C is reversibly frozen to ice at 0.00 ◦ C at
a constant pressure of 1.000 atm.
Solution
q ∆H (2.000 mol)
18.02 g mol −1
−333.5 J g −1
−1.202 × 10 4 J
Since the enthalpy is a state function, we can calculate ∆H for a given process by
calculating ∆H for any process having the same initial and final states.
E X A M P L E 2.26
Calculate ∆H for the change of state of 1.000 mol of helium from a volume of 5.000 L and
a temperature of 298.15 K to a volume of 10.000 L and a temperature of 373.15 K. Assume
that C P,m 5R/2 and assume that the gas is ideal.
Solution
The value of ∆H is path-independent. For purposes of calculation, assume that the gas first
expands isothermally and reversibly to a pressure equal to the final pressure (step 1), and is
then heated at constant pressure to its final temperature (step 2). Since the enthalpy depends