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2.13: Untitled Page 25

  • Page ID
    18158
  • Chapter 2

    The units of C are joule/(mol K), and the units of temperature are degrees p

    Kelvin. For chlorine, the values of the coefficients are: A

    1

    22.85 , A 2 0 06543

    .

    ,

    4

    A  

     

    3

    1.2517 10

    ,

    7

    A 4 1.1484 10 , and

    11

    A

    4.0946 10

    5

    . What are the

    units of the coefficients? Find the values of the coefficients to compute the heat capacity of chlorine in cal/g C, using temperature in degrees Rankine.

    Section 2.4

    2‐17. A standard cubic foot, or scf, of gas represents one cubic foot of gas at one atmosphere and 273.16 K. This means that a standard cubic foot is a convenience unit for moles. This is easy to see in terms of an ideal gas for which the equation of state is given by (see Sec. 5.1)

    pV

    nRT

    The number of moles in one standard cubic foot of an ideal gas can be calculated as

    p

    = one atmosphere

    n pV RT

    V

    = one cubic foot

     T =273.16 K

    and for a non‐ideal gas one must use an appropriate equation of state (Sandler, 2006). In this problem you are asked to determine the number of moles that are equivalent to one scf of an ideal gas (see Sec. 5.1).

    2‐18. Energy is sometimes expressed as 2

    v / 2 g although this term does not have

    the units of energy. What are the units of this term and why would it be used to represent energy? Think about the fact that  gh represents the gravitational potential energy per unit volume of a fluid and that h is often used as a convenience unit for gravitational potential energy. Remember that 1

    2

    v

    2

    represents the kinetic energy per unit volume where v is determined by 2

    v  v v

    and consider the case for which the fluid density is a constant.

    Section 2.5

    2‐19. Find the dimensions of the following product

    D v

    Re

    Units

    37

    in which  is the density of a fluid, D is the diameter of a pipe, v is the velocity of the fluid inside the pipe, and  is the viscosity of the fluid.

    2‐20. A useful dimensionless number used in characterization of gas‐liquid flows is the Weber number, defined as

    2

    D U

    We

    b

    b

    where  is the density of the fluid,

    is the diameter of a bubble, U is the

    b

    D

    b

    velocity of the bubble with respect to the surrounding liquid, and  is the interfacial gas‐liquid tension. Verify that the Weber number is dimensionless.

    2‐21. Given a gas mixture consisting of 5 lb of methane, 10 lb of ethane, m

    m

    5 lb of propane, and 3 lb of butane, determine the number of moles of m

    m

    each component in the mixture.

    Section 2.6

    2‐22. Given the following 3  3 matrices

     3

    5 4 

     2

    1

    3 

    A

    6

    1

    9

    B

    1

    2 5

     4 3

    2 

    

     3 5 2 

    determine A  B and A  3B .

    2‐23. Given the following 1 4 row matrices

    a

      3 1 5 6  ,

    b

      6 2 0 4 

    determine 2a  b .

    Note: Problems marked with the symbol  will be difficult to solve without the use of computer software.

    2‐24. Compute the 4  4 matrix defined by A  B  C where A, B and C are given by

    38