Interpretation:
The units in equation 4.18-4.25 are to be shown consistent on both the sides of each equation.
Concept introduction:
The
Answer to Problem 4.31E
The units in equation 4.18-4.25 have been shown consistent on both the sides of each equation.
Explanation of Solution
The equation 4.18 is shown below.
Where,
•
•
•
•
The units of internal energy, temperature, entropy, pressure and volume is
Substitute the units of internal energy and entropy in the left hand side expression as shown below.
Thus, the unit obtained is Kelvin which is the unit of temperature. Thus, the units are consistent on the either side of the equation.
The equation 4.19 is shown below.
Where,
•
•
•
•
The units of internal energy and entropy can also be expressed in per molecule, the units of internal energy and entropy is
Substitute the units of internal energy and volume in the left hand side expression as shown below.
The units of internal energy joule can be substituted as
Thus, the unit obtained is Pascal which is the unit of pressure. Thus, the units are consistent on the either side of the equation.
The equation 4.20 is shown below.
Where,
•
•
•
•
The units of enthalpy, temperature, entropy, pressure and volume is
Substitute the units of enthalpy and entropy in the left hand side expression as shown below.
Thus, the unit obtained is Kelvin which is the unit of temperature. Thus, the units are consistent on the either side of the equation.
The equation 4.21 is shown below.
Where,
•
•
•
•
The units of enthalpy and entropy can also be expressed in per molecule, the units of enthalpy and entropy is
Substitute the units of enthalpy and pressure in the left hand side expression as shown below.
The units of enthalpy joule can be substituted as
Thus, the unit obtained is cubic meter which is the unit of volume. Thus, the units are consistent on the either side of the equation.
The equation 4.22 is shown below.
Where,
•
•
•
•
The units of Helmholtz energy, temperature, entropy, pressure and volume is
Substitute the units of Helmholtz energy and temperature in the left hand side expression as shown below.
Thus, the unit obtained is
The equation 4.23 is shown below.
Where,
•
•
•
•
The units of Helmholtz energy and entropy can also be expressed in per molecule, the units of Helmholtz energy and entropy is
Substitute the units of Helmholtz energy and volume in the left hand side expression as shown below.
The units of Helmholtz energy joule can be substituted as
Thus, the unit obtained is Pascal which is the unit of pressure. Thus, the units are consistent on the either side of the equation.
The equation 4.24 is shown below.
Where,
•
•
•
•
The units of Gibbs energy and entropy can also be expressed in per molecule, the units of Gibbs energy and entropy is
Substitute the units of Gibbs energy and temperature in the left hand side expression as shown below.
Thus, the unit obtained is
The equation 4.25 is shown below.
Where,
•
•
•
•
The units of Gibbs energy and entropy can also be expressed in per molecule, the units of Gibbs energy and entropy is
Substitute the units of Gibbs energy and pressure in the left hand side expression as shown below.
The units of Gibbs energy joule can be substituted as
Thus, the unit obtained is cubic meter which is the unit of volume. Thus, the units are consistent on the either side of the equation.
The units in equation 4.18-4.25 have been shown consistent on both the sides of each equation.
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