69243318 Solved Problems in Thermodynamics

Solved Problems in Thermodynamic Property Relations 1.) Verify the validity of the Maxwell relation IV (Eq. 3 .20) for steam at 250°C and 300 kPa. Solution:

                        [ ]   [      ] ⁄       ⁄                         ⁄   ⁄  

from steam tables:

2.) Using the Clausius-Clapeyron equation, estimate the value of the enthalpy of vaporization of  refrigerant-134a at 20°C.

      (  )    ⁄  ⁄                   ⁄      ⁄⁄ ⁄  Solution:

from refrigerant tables:

substituting these values to the equation for h for h fg :

The actual value of h of h fg  is 181.09 kJ/kg.

3.) Estimate the saturation pressure of refrigerant-134a at-50°F, using the data available in the refrigerant tables. Solution: Using the Clausius-Clapeyron equation the saturation pressure can be extrapolated in the absence of a compete table.

         ⁄⁄     

integrating the Clausius-Clapeyron equation:

let T 1 = -40°F and T 2 = -50°F

The actual value of the saturation pressure p2 at -50°F is 5.505 psia.

4.) Show that

  

for an ideal gas.

Solution: This relation is proved by showing that the right-hand side of (5.31) is equivalent to the gas constant R of the ideal gas:

subtituting:

                            

5.) Show that the Joule-Thompson coefficient of an ideal gas is zero.

    *+ ⁄          *+  [ ]   

Solution:

For an ideal gas

, and thus

substituting:

6.) Determine the enthalpy change and entropy change of oxygen per unit mole as it undergoes a change of state from 220°K and 5 MPa to 300°K and 10 MPa (a) by assuming ideal-gas  behavior and (b) by accounting for the deviation from ideal-gas behavior. Solution: (a) The enthalpy values at the initial and the final temperatures can be determined from the ideal-gas table at the specified temperatures:

 ⁄ ( ())     ⁄ ̅ ̅ ̅ ̅    ̅ ∫ ̅     ̅ ̅  ⁄ ⁄                  ̅ ̅  ⁄         }        

The entropy depends on both temperature and pressure even for ideal gases. Under the ideal-gas assumption, the entropy change of ox ygen is determined from

where:

(b) The deviation from the ideal-gas behavior can be accounted for by determining the enthalpy and entropy from the generalized charts at each state:

and

Then,

and

     }                  (  )                ⁄   ⁄ ⁄  ̅ ̅ ̅ ̅                      ⁄̅  ̅ ⁄⁄

7.) Using  p-v-T data for saturated water, calculate the (a) latent heat of vaporization at 100°C and (b) s g  –  s f . Solution: (a)

           +    ⁄⁄*

from steam tables:

This agrees very closely with the value read from the steam tables, h fg  = 2257 kJ/kg.

(b)

     ⁄  ⁄  

8.) Determine the u g  –  u f  of water at 100°C.

          ( ) ⁄    ⁄       ⁄

Solution:

since vaporization occurs at constant pressure:

from steam tables:

9.) For liquid water at 1 atm and 20°C, estimate the percent error in cv that would result if it were assumed that c p = cv. Solution:

             ⁄                              ⁄      ⁄ ⁄      ⁄       ⁄⁄   

10.) Using h fg , v fg  and  psat at 10°F from the refrigerant-134a tables, estimate the saturation  pressure at 20°F. Solution:

 

integrating the above equation yields:

:

 ⁄    ⁄   

Reference: th Y. A. Yunus and M. A. Boles. Thermodynamics: An Engineering Approach, 4 Ed. New York: McGraw-Hill, 2002. th

M. J. Moran and H. N. Shapiro. Fundamentals of Engineering Thermodynamics, 5 Ed. John Wiley & Sons, Inc., 2004.